id sid tid token lemma pos iajs-2566 1 1 ibn ibn PROPN iajs-2566 1 2 al al PROPN iajs-2566 1 3 - - PUNCT iajs-2566 1 4 haitham haitham PROPN iajs-2566 1 5 jour jour X iajs-2566 1 6 . . PROPN iajs-2566 1 7 for for ADP iajs-2566 1 8 pure pure ADJ iajs-2566 1 9 & & CCONJ iajs-2566 1 10 appl appl PROPN iajs-2566 1 11 . . PUNCT iajs-2566 2 1 sci sci PROPN iajs-2566 2 2 . . PROPN iajs-2566 3 1 34 34 NUM iajs-2566 3 2 ( ( PUNCT iajs-2566 3 3 1 1 NUM iajs-2566 3 4 ) ) PUNCT iajs-2566 3 5 2021 2021 NUM iajs-2566 4 1 47 47 NUM iajs-2566 4 2 Ψ­ Ψ­ NOUN iajs-2566 4 3 generalize generalize VERB iajs-2566 4 4 partial partial ADJ iajs-2566 4 5 metric metric ADJ iajs-2566 4 6 spaces space NOUN iajs-2566 4 7 norhan norhan PROPN iajs-2566 4 8 i. i. PROPN iajs-2566 4 9 abdullah abdullah PROPN iajs-2566 4 10 laith laith PROPN iajs-2566 4 11 k. k. PROPN iajs-2566 4 12 shaakir shaakir PROPN iajs-2566 4 13 department department PROPN iajs-2566 4 14 of of ADP iajs-2566 4 15 mathematics mathematics PROPN iajs-2566 4 16 , , PUNCT iajs-2566 4 17 college college NOUN iajs-2566 4 18 of of ADP iajs-2566 4 19 computer computer NOUN iajs-2566 4 20 and and CCONJ iajs-2566 4 21 mathematics mathematic NOUN iajs-2566 4 22 sciences sciences PROPN iajs-2566 4 23 , , PUNCT iajs-2566 4 24 university university NOUN iajs-2566 4 25 of of ADP iajs-2566 4 26 tikrit tikrit NOUN iajs-2566 4 27 , , PUNCT iajs-2566 4 28 tikrit tikrit NOUN iajs-2566 4 29 , , PUNCT iajs-2566 4 30 iraq iraq PROPN iajs-2566 4 31 esamanorhan221@gmail.com esamanorhan221@gmail.com X iajs-2566 5 1 dr.laithkhaleel@tu.edu.iq dr.laithkhaleel@tu.edu.iq PROPN iajs-2566 5 2 abstract abstract ADJ iajs-2566 5 3 the the DET iajs-2566 5 4 purpose purpose NOUN iajs-2566 5 5 of of ADP iajs-2566 5 6 this this DET iajs-2566 5 7 research research NOUN iajs-2566 5 8 is be AUX iajs-2566 5 9 to to PART iajs-2566 5 10 introduce introduce VERB iajs-2566 5 11 a a DET iajs-2566 5 12 concept concept NOUN iajs-2566 5 13 of of ADP iajs-2566 5 14 general general ADJ iajs-2566 5 15 partial partial ADJ iajs-2566 5 16 metric metric ADJ iajs-2566 5 17 spaces space NOUN iajs-2566 5 18 as as ADP iajs-2566 5 19 a a DET iajs-2566 5 20 generalization generalization NOUN iajs-2566 5 21 of of ADP iajs-2566 5 22 partial partial ADJ iajs-2566 5 23 metric metric ADJ iajs-2566 5 24 space space NOUN iajs-2566 5 25 , , PUNCT iajs-2566 5 26 give give VERB iajs-2566 5 27 some some DET iajs-2566 5 28 results result NOUN iajs-2566 5 29 and and CCONJ iajs-2566 5 30 properties property NOUN iajs-2566 5 31 and and CCONJ iajs-2566 5 32 find find VERB iajs-2566 5 33 relations relation NOUN iajs-2566 5 34 between between ADP iajs-2566 5 35 the the DET iajs-2566 5 36 general general ADJ iajs-2566 5 37 partial partial ADJ iajs-2566 5 38 metric metric ADJ iajs-2566 5 39 space space NOUN iajs-2566 5 40 , , PUNCT iajs-2566 5 41 partial partial ADJ iajs-2566 5 42 metric metric ADJ iajs-2566 5 43 spaces space NOUN iajs-2566 5 44 and and CCONJ iajs-2566 5 45 d d NOUN iajs-2566 5 46 - - ADJ iajs-2566 5 47 metric metric ADJ iajs-2566 5 48 spaces space NOUN iajs-2566 5 49 . . PUNCT iajs-2566 6 1 keywords keyword NOUN iajs-2566 6 2 : : PUNCT iajs-2566 6 3 partial partial ADJ iajs-2566 6 4 metric metric ADJ iajs-2566 6 5 space space NOUN iajs-2566 6 6 , , PUNCT iajs-2566 6 7 d d ADJ iajs-2566 6 8 - - ADJ iajs-2566 6 9 metric metric ADJ iajs-2566 6 10 space space NOUN iajs-2566 6 11 , , PUNCT iajs-2566 6 12 general general ADJ iajs-2566 6 13 partial partial ADJ iajs-2566 6 14 metric metric ADJ iajs-2566 6 15 space space NOUN iajs-2566 6 16 . . PUNCT iajs-2566 7 1 1 1 NUM iajs-2566 7 2 introduction introduction NOUN iajs-2566 7 3 and and CCONJ iajs-2566 7 4 preliminaries preliminary NOUN iajs-2566 7 5 metric metric ADJ iajs-2566 7 6 spaces space NOUN iajs-2566 7 7 are be AUX iajs-2566 7 8 very very ADV iajs-2566 7 9 important important ADJ iajs-2566 7 10 in in ADP iajs-2566 7 11 mathematics mathematic NOUN iajs-2566 7 12 introduced introduce VERB iajs-2566 7 13 and and CCONJ iajs-2566 7 14 studied study VERB iajs-2566 7 15 by by ADP iajs-2566 7 16 the the DET iajs-2566 7 17 french french ADJ iajs-2566 7 18 mathematicians mathematician NOUN iajs-2566 7 19 . . PUNCT iajs-2566 8 1 many many ADJ iajs-2566 8 2 researchers researcher NOUN iajs-2566 8 3 tried try VERB iajs-2566 8 4 to to PART iajs-2566 8 5 generalized generalized VERB iajs-2566 8 6 the the DET iajs-2566 8 7 metric metric ADJ iajs-2566 8 8 space space NOUN iajs-2566 8 9 to to ADP iajs-2566 8 10 different different ADJ iajs-2566 8 11 types type NOUN iajs-2566 8 12 for for ADP iajs-2566 8 13 example example NOUN iajs-2566 8 14 , , PUNCT iajs-2566 8 15 b b X iajs-2566 8 16 - - PUNCT iajs-2566 8 17 metric metric ADJ iajs-2566 8 18 space space NOUN iajs-2566 8 19 defined define VERB iajs-2566 8 20 by by ADP iajs-2566 8 21 stefan stefan PROPN iajs-2566 8 22 czerwik czerwik PROPN iajs-2566 9 1 [ [ X iajs-2566 9 2 1 1 NUM iajs-2566 9 3 ] ] PUNCT iajs-2566 9 4 , , PUNCT iajs-2566 9 5 g g NOUN iajs-2566 9 6 - - PUNCT iajs-2566 9 7 metric metric ADJ iajs-2566 9 8 space space NOUN iajs-2566 9 9 defined define VERB iajs-2566 9 10 by by ADP iajs-2566 9 11 mustafa mustafa PROPN iajs-2566 9 12 and and CCONJ iajs-2566 9 13 sims sim NOUN iajs-2566 9 14 [ [ X iajs-2566 9 15 2 2 NUM iajs-2566 9 16 ] ] PUNCT iajs-2566 9 17 , , PUNCT iajs-2566 9 18 2 2 NUM iajs-2566 9 19 - - PUNCT iajs-2566 9 20 metric metric ADJ iajs-2566 9 21 space space NOUN iajs-2566 9 22 defined define VERB iajs-2566 9 23 by by ADP iajs-2566 9 24 gahler gahler NOUN iajs-2566 10 1 [ [ X iajs-2566 10 2 3 3 NUM iajs-2566 10 3 ] ] PUNCT iajs-2566 10 4 , , PUNCT iajs-2566 10 5 d*-metric d*-metric ADJ iajs-2566 10 6 space[4 space[4 NUM iajs-2566 10 7 ] ] PUNCT iajs-2566 10 8 , , PUNCT iajs-2566 10 9 partial partial ADJ iajs-2566 10 10 metric metric ADJ iajs-2566 10 11 space space NOUN iajs-2566 10 12 defined define VERB iajs-2566 10 13 by by ADP iajs-2566 10 14 mathews[5 mathews[5 NOUN iajs-2566 10 15 ] ] PUNCT iajs-2566 10 16 and and CCONJ iajs-2566 10 17 d d ADJ iajs-2566 10 18 - - ADJ iajs-2566 10 19 metric metric ADJ iajs-2566 10 20 space space NOUN iajs-2566 10 21 defined define VERB iajs-2566 10 22 by by ADP iajs-2566 10 23 dhage dhage NOUN iajs-2566 11 1 [ [ X iajs-2566 11 2 11 11 NUM iajs-2566 11 3 ] ] PUNCT iajs-2566 11 4 first first ADV iajs-2566 11 5 , , PUNCT iajs-2566 11 6 give give VERB iajs-2566 11 7 some some DET iajs-2566 11 8 definitions definition NOUN iajs-2566 11 9 and and CCONJ iajs-2566 11 10 properties property NOUN iajs-2566 11 11 of of ADP iajs-2566 11 12 the the DET iajs-2566 11 13 partial partial ADJ iajs-2566 11 14 metric metric ADJ iajs-2566 11 15 spaces space NOUN iajs-2566 11 16 that that PRON iajs-2566 11 17 can can AUX iajs-2566 11 18 be be AUX iajs-2566 11 19 found find VERB iajs-2566 11 20 in in ADP iajs-2566 11 21 [ [ X iajs-2566 11 22 510 510 NUM iajs-2566 11 23 ] ] PUNCT iajs-2566 11 24 a a DET iajs-2566 11 25 non non ADJ iajs-2566 11 26 - - ADJ iajs-2566 11 27 empty empty ADJ iajs-2566 11 28 set set NOUN iajs-2566 11 29 π‘Œ π‘Œ PROPN iajs-2566 11 30 is be AUX iajs-2566 11 31 said say VERB iajs-2566 11 32 to to PART iajs-2566 11 33 be be AUX iajs-2566 11 34 partial partial ADJ iajs-2566 11 35 metric metric ADJ iajs-2566 11 36 space space NOUN iajs-2566 11 37 if if SCONJ iajs-2566 11 38 there there PRON iajs-2566 11 39 exists exist VERB iajs-2566 11 40 a a DET iajs-2566 11 41 function function NOUN iajs-2566 11 42 𝑝 𝑝 NOUN iajs-2566 11 43 : : PUNCT iajs-2566 11 44 π‘Œ2 π‘Œ2 NOUN iajs-2566 11 45 β†’ β†’ PUNCT iajs-2566 12 1 [ [ X iajs-2566 12 2 0 0 NUM iajs-2566 12 3 , , PUNCT iajs-2566 12 4 ∞ ∞ PROPN iajs-2566 12 5 ) ) PUNCT iajs-2566 12 6 satisfies satisfy VERB iajs-2566 12 7 the the DET iajs-2566 12 8 following follow VERB iajs-2566 12 9 condition condition NOUN iajs-2566 12 10 : : PUNCT iajs-2566 13 1 p1 p1 NOUN iajs-2566 13 2 𝛼 𝛼 NOUN iajs-2566 13 3 = = SYM iajs-2566 13 4 𝛽 𝛽 PROPN iajs-2566 13 5 ↔ ↔ PROPN iajs-2566 13 6 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 13 7 , , PUNCT iajs-2566 13 8 𝛼 𝛼 NOUN iajs-2566 13 9 ) ) PUNCT iajs-2566 13 10 = = SYM iajs-2566 13 11 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 13 12 , , PUNCT iajs-2566 13 13 𝛽 𝛽 NOUN iajs-2566 13 14 ) ) PUNCT iajs-2566 14 1 = = SYM iajs-2566 14 2 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 14 3 , , PUNCT iajs-2566 14 4 𝛽 𝛽 NOUN iajs-2566 14 5 ) ) PUNCT iajs-2566 14 6 p2 p2 PROPN iajs-2566 14 7 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 14 8 , , PUNCT iajs-2566 14 9 𝛼 𝛼 NOUN iajs-2566 14 10 ) ) PUNCT iajs-2566 14 11 ≀ ≀ PROPN iajs-2566 14 12 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 14 13 , , PUNCT iajs-2566 14 14 𝛽 𝛽 NOUN iajs-2566 14 15 ) ) PUNCT iajs-2566 14 16 p3 p3 PROPN iajs-2566 14 17 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 14 18 , , PUNCT iajs-2566 14 19 𝛽 𝛽 NOUN iajs-2566 14 20 ) ) PUNCT iajs-2566 14 21 = = SYM iajs-2566 14 22 𝑝 𝑝 PROPN iajs-2566 14 23 ( ( PUNCT iajs-2566 14 24 𝛽 𝛽 PROPN iajs-2566 14 25 , , PUNCT iajs-2566 14 26 𝛼 𝛼 NOUN iajs-2566 14 27 ) ) PUNCT iajs-2566 14 28 p4 p4 PROPN iajs-2566 14 29 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 14 30 , , PUNCT iajs-2566 14 31 𝛽 𝛽 NOUN iajs-2566 14 32 ) ) PUNCT iajs-2566 14 33 ≀ ≀ PROPN iajs-2566 14 34 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 14 35 , , PUNCT iajs-2566 14 36 πœ‡ πœ‡ ADP iajs-2566 14 37 ) ) PUNCT iajs-2566 14 38 + + SYM iajs-2566 14 39 𝑝 𝑝 NOUN iajs-2566 14 40 ( ( PUNCT iajs-2566 14 41 πœ‡ πœ‡ ADP iajs-2566 14 42 , , PUNCT iajs-2566 14 43 𝛽 𝛽 NOUN iajs-2566 14 44 ) ) PUNCT iajs-2566 14 45 – – PUNCT iajs-2566 14 46 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 14 47 , , PUNCT iajs-2566 14 48 πœ‡ πœ‡ NOUN iajs-2566 14 49 ) ) PUNCT iajs-2566 14 50 βˆ€ βˆ€ NOUN iajs-2566 14 51 𝛼 𝛼 NOUN iajs-2566 14 52 , , PUNCT iajs-2566 14 53 𝛽 𝛽 NOUN iajs-2566 14 54 and and CCONJ iajs-2566 14 55 πœ‡ πœ‡ ADP iajs-2566 14 56 ∈ ∈ PROPN iajs-2566 14 57 y y PROPN iajs-2566 14 58 , , PUNCT iajs-2566 14 59 where where SCONJ iajs-2566 14 60 𝑝 𝑝 NOUN iajs-2566 14 61 is be AUX iajs-2566 14 62 a a DET iajs-2566 14 63 partial partial ADJ iajs-2566 14 64 metric metric NOUN iajs-2566 14 65 on on ADP iajs-2566 14 66 π‘Œ π‘Œ PROPN iajs-2566 14 67 . . PUNCT iajs-2566 15 1 a a DET iajs-2566 15 2 basic basic ADJ iajs-2566 15 3 example example NOUN iajs-2566 15 4 of of ADP iajs-2566 15 5 a a DET iajs-2566 15 6 partial partial ADJ iajs-2566 15 7 metric metric ADJ iajs-2566 15 8 space space NOUN iajs-2566 15 9 is be AUX iajs-2566 15 10 ( ( PUNCT iajs-2566 15 11 𝑅+ 𝑅+ PROPN iajs-2566 15 12 , , PUNCT iajs-2566 15 13 𝑝 𝑝 NOUN iajs-2566 15 14 ) ) PUNCT iajs-2566 15 15 , , PUNCT iajs-2566 15 16 where where SCONJ iajs-2566 15 17 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 15 18 , , PUNCT iajs-2566 15 19 𝛽 𝛽 NOUN iajs-2566 15 20 ) ) PUNCT iajs-2566 15 21 = = SYM iajs-2566 15 22 max{𝛼 max{𝛼 NOUN iajs-2566 15 23 , , PUNCT iajs-2566 15 24 𝛽 𝛽 NOUN iajs-2566 15 25 } } PUNCT iajs-2566 15 26 βˆ€π›Ό βˆ€π›Ό PROPN iajs-2566 15 27 , , PUNCT iajs-2566 15 28 𝛽 𝛽 PROPN iajs-2566 15 29 ∈ ∈ PROPN iajs-2566 15 30 𝑅+ 𝑅+ PROPN iajs-2566 15 31 ibn ibn PROPN iajs-2566 15 32 al al PROPN iajs-2566 15 33 haitham haitham PROPN iajs-2566 15 34 journal journal PROPN iajs-2566 15 35 for for ADP iajs-2566 15 36 pure pure ADJ iajs-2566 15 37 and and CCONJ iajs-2566 15 38 applied apply VERB iajs-2566 15 39 science science NOUN iajs-2566 15 40 journal journal PROPN iajs-2566 15 41 homepage homepage NOUN iajs-2566 15 42 : : PUNCT iajs-2566 15 43 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index NOUN iajs-2566 15 44 doi doi NOUN iajs-2566 15 45 : : PUNCT iajs-2566 15 46 10.30526/34.1.2566 10.30526/34.1.2566 NUM iajs-2566 15 47 article article NOUN iajs-2566 15 48 history history NOUN iajs-2566 15 49 : : PUNCT iajs-2566 15 50 received receive VERB iajs-2566 15 51 2 2 NUM iajs-2566 15 52 , , PUNCT iajs-2566 15 53 february february PROPN iajs-2566 15 54 , , PUNCT iajs-2566 15 55 2020 2020 NUM iajs-2566 15 56 , , PUNCT iajs-2566 15 57 accepted20 accepted20 ADJ iajs-2566 15 58 , , PUNCT iajs-2566 15 59 february february PROPN iajs-2566 15 60 , , PUNCT iajs-2566 15 61 2020 2020 NUM iajs-2566 15 62 , , PUNCT iajs-2566 15 63 published publish VERB iajs-2566 15 64 in in ADP iajs-2566 15 65 january january PROPN iajs-2566 15 66 2021 2021 NUM iajs-2566 15 67 mailto:esamanorhan221@gmail.com mailto:esamanorhan221@gmail.com X iajs-2566 15 68 mailto:dr.laithkhaleel@tu.edu.iq mailto:dr.laithkhaleel@tu.edu.iq NOUN iajs-2566 15 69 48 48 NUM iajs-2566 15 70 ibn ibn PROPN iajs-2566 15 71 al al PROPN iajs-2566 15 72 - - PUNCT iajs-2566 15 73 haitham haitham PROPN iajs-2566 15 74 jour jour X iajs-2566 15 75 . . PROPN iajs-2566 16 1 for for ADP iajs-2566 16 2 pure pure ADJ iajs-2566 16 3 & & CCONJ iajs-2566 16 4 appl appl PROPN iajs-2566 16 5 . . PUNCT iajs-2566 17 1 sci sci PROPN iajs-2566 17 2 . . PROPN iajs-2566 18 1 34 34 NUM iajs-2566 18 2 ( ( PUNCT iajs-2566 18 3 1 1 NUM iajs-2566 18 4 ) ) PUNCT iajs-2566 18 5 2021 2021 NUM iajs-2566 18 6 also also ADV iajs-2566 18 7 , , PUNCT iajs-2566 18 8 the the DET iajs-2566 18 9 partial partial ADJ iajs-2566 18 10 metric metric ADJ iajs-2566 18 11 space space NOUN iajs-2566 18 12 p p NOUN iajs-2566 18 13 on on ADP iajs-2566 18 14 π‘Œ π‘Œ PROPN iajs-2566 18 15 generates generate VERB iajs-2566 18 16 a a DET iajs-2566 18 17 𝑇0 𝑇0 NOUN iajs-2566 18 18 topology topology NOUN iajs-2566 18 19 πœπ‘on πœπ‘on NOUN iajs-2566 18 20 π‘Œ π‘Œ PROPN iajs-2566 18 21 , , PUNCT iajs-2566 18 22 which which PRON iajs-2566 18 23 has have VERB iajs-2566 18 24 as as ADP iajs-2566 18 25 a a DET iajs-2566 18 26 base base NOUN iajs-2566 18 27 of of ADP iajs-2566 18 28 family family NOUN iajs-2566 19 1 open open ADJ iajs-2566 19 2 balls{𝐡𝑝(𝛼 balls{𝐡𝑝(𝛼 PROPN iajs-2566 19 3 , , PUNCT iajs-2566 19 4 πœ– πœ– PROPN iajs-2566 19 5 ) ) PUNCT iajs-2566 19 6 ∢ ∢ NOUN iajs-2566 19 7 𝛼 𝛼 NOUN iajs-2566 19 8 ∈ ∈ PROPN iajs-2566 19 9 π‘Œ π‘Œ PROPN iajs-2566 19 10 , , PUNCT iajs-2566 19 11 πœ– πœ– X iajs-2566 19 12 > > X iajs-2566 19 13 0 0 NUM iajs-2566 19 14 } } PUNCT iajs-2566 19 15 , , PUNCT iajs-2566 19 16 where where SCONJ iajs-2566 19 17 𝐡𝑝(𝛼 𝐡𝑝(𝛼 ADJ iajs-2566 19 18 , , PUNCT iajs-2566 19 19 νœ€ νœ€ NOUN iajs-2566 19 20 ) ) PUNCT iajs-2566 19 21 = = NOUN iajs-2566 19 22 { { PUNCT iajs-2566 19 23 𝛽 𝛽 NOUN iajs-2566 19 24 ∈ ∈ PROPN iajs-2566 19 25 π‘Œ π‘Œ PROPN iajs-2566 19 26 : : PUNCT iajs-2566 20 1 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 20 2 , , PUNCT iajs-2566 20 3 𝛽 𝛽 NOUN iajs-2566 20 4 ) ) PUNCT iajs-2566 20 5 < < X iajs-2566 20 6 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 20 7 , , PUNCT iajs-2566 20 8 𝛼 𝛼 NOUN iajs-2566 20 9 ) ) PUNCT iajs-2566 20 10 + + CCONJ iajs-2566 20 11 Ο΅ Ο΅ X iajs-2566 20 12 } } PUNCT iajs-2566 20 13 βˆ€ βˆ€ NUM iajs-2566 20 14 𝛼 𝛼 ADP iajs-2566 20 15 ∈ ∈ PROPN iajs-2566 20 16 y y PROPN iajs-2566 20 17 and and CCONJ iajs-2566 20 18 πœ– πœ– X iajs-2566 20 19 > > X iajs-2566 20 20 0 0 NUM iajs-2566 20 21 . . PUNCT iajs-2566 21 1 ( ( PUNCT iajs-2566 21 2 see see VERB iajs-2566 21 3 [ [ X iajs-2566 21 4 9 9 NUM iajs-2566 21 5 ] ] PUNCT iajs-2566 21 6 ) ) PUNCT iajs-2566 21 7 the the DET iajs-2566 21 8 sequence sequence NOUN iajs-2566 21 9 { { PUNCT iajs-2566 21 10 𝛼n 𝛼n NOUN iajs-2566 21 11 } } PUNCT iajs-2566 21 12 in in ADP iajs-2566 21 13 a a DET iajs-2566 21 14 partial partial ADJ iajs-2566 21 15 metric metric ADJ iajs-2566 21 16 space space NOUN iajs-2566 21 17 ( ( PUNCT iajs-2566 21 18 π‘Œ π‘Œ PROPN iajs-2566 21 19 , , PUNCT iajs-2566 21 20 𝑝 𝑝 NOUN iajs-2566 21 21 ) ) PUNCT iajs-2566 21 22 converge converge NOUN iajs-2566 21 23 sequence sequence NOUN iajs-2566 21 24 if if SCONJ iajs-2566 21 25 π‘™π‘–π‘šπ‘›β†’βˆž π‘™π‘–π‘šπ‘›β†’βˆž PROPN iajs-2566 21 26 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 21 27 , , PUNCT iajs-2566 21 28 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 21 29 ) ) PUNCT iajs-2566 21 30 = = SYM iajs-2566 21 31 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 21 32 , , PUNCT iajs-2566 21 33 𝛼 𝛼 NOUN iajs-2566 21 34 ) ) PUNCT iajs-2566 21 35 the the DET iajs-2566 21 36 sequence sequence NOUN iajs-2566 21 37 { { PUNCT iajs-2566 21 38 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 21 39 } } PUNCT iajs-2566 21 40 in in ADP iajs-2566 21 41 a a DET iajs-2566 21 42 partial partial ADJ iajs-2566 21 43 metric metric ADJ iajs-2566 21 44 space space NOUN iajs-2566 21 45 ( ( PUNCT iajs-2566 21 46 π‘Œ π‘Œ PROPN iajs-2566 21 47 , , PUNCT iajs-2566 21 48 𝑝 𝑝 NOUN iajs-2566 21 49 ) ) PUNCT iajs-2566 21 50 is be AUX iajs-2566 21 51 said say VERB iajs-2566 21 52 to to PART iajs-2566 21 53 be be AUX iajs-2566 21 54 cauchy cauchy ADJ iajs-2566 21 55 sequences sequence NOUN iajs-2566 21 56 if if SCONJ iajs-2566 21 57 lim𝑛,π‘š lim𝑛,π‘š NUM iajs-2566 21 58 β†’βˆž β†’βˆž PROPN iajs-2566 21 59 𝑝(𝛼𝑛 𝑝(𝛼𝑛 PROPN iajs-2566 21 60 , , PUNCT iajs-2566 21 61 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 21 62 ) ) PUNCT iajs-2566 21 63 exists exist VERB iajs-2566 21 64 ( ( PUNCT iajs-2566 21 65 finite finite PROPN iajs-2566 21 66 ) ) PUNCT iajs-2566 21 67 . . PUNCT iajs-2566 22 1 the the DET iajs-2566 22 2 partial partial ADJ iajs-2566 22 3 metric metric ADJ iajs-2566 22 4 space space NOUN iajs-2566 22 5 ( ( PUNCT iajs-2566 22 6 π‘Œ π‘Œ PROPN iajs-2566 22 7 , , PUNCT iajs-2566 22 8 𝑝 𝑝 NOUN iajs-2566 22 9 ) ) PUNCT iajs-2566 22 10 is be AUX iajs-2566 22 11 said say VERB iajs-2566 22 12 to to PART iajs-2566 22 13 be be AUX iajs-2566 22 14 complete complete ADJ iajs-2566 22 15 if if SCONJ iajs-2566 22 16 every every DET iajs-2566 22 17 cauchy cauchy ADJ iajs-2566 22 18 sequence sequence NOUN iajs-2566 22 19 { { PUNCT iajs-2566 22 20 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 22 21 } } PUNCT iajs-2566 22 22 convergent convergent NOUN iajs-2566 22 23 to to ADP iajs-2566 22 24 a a DET iajs-2566 22 25 point point NOUN iajs-2566 22 26 𝛼 𝛼 NOUN iajs-2566 22 27 in in ADP iajs-2566 22 28 y. y. PROPN iajs-2566 22 29 a a DET iajs-2566 22 30 mapping mapping NOUN iajs-2566 22 31 𝐹 𝐹 PROPN iajs-2566 22 32 : : PUNCT iajs-2566 22 33 ( ( PUNCT iajs-2566 22 34 π‘Œ π‘Œ PROPN iajs-2566 22 35 , , PUNCT iajs-2566 22 36 𝑝 𝑝 NOUN iajs-2566 22 37 ) ) PUNCT iajs-2566 22 38 β†’ β†’ SYM iajs-2566 22 39 ( ( PUNCT iajs-2566 22 40 π‘Œ π‘Œ PROPN iajs-2566 22 41 ` ` PUNCT iajs-2566 22 42 , , PUNCT iajs-2566 22 43 𝑝 𝑝 NOUN iajs-2566 22 44 ` ` PUNCT iajs-2566 22 45 ) ) PUNCT iajs-2566 22 46 is be AUX iajs-2566 22 47 said say VERB iajs-2566 22 48 to to PART iajs-2566 22 49 be be AUX iajs-2566 22 50 continuous continuous ADJ iajs-2566 22 51 at at ADP iajs-2566 22 52 𝛼0∈y 𝛼0∈y PROPN iajs-2566 22 53 , , PUNCT iajs-2566 22 54 if if SCONJ iajs-2566 22 55 for for ADP iajs-2566 22 56 everyπœ– everyπœ– NOUN iajs-2566 22 57 > > X iajs-2566 22 58 0 0 PROPN iajs-2566 22 59 , , PUNCT iajs-2566 22 60 there there PRON iajs-2566 22 61 exists exist VERB iajs-2566 22 62 𝛿 𝛿 PROPN iajs-2566 22 63 > > X iajs-2566 22 64 0 0 NUM iajs-2566 22 65 such such ADJ iajs-2566 22 66 that that DET iajs-2566 22 67 f(b𝑝(𝛼0 f(b𝑝(𝛼0 NOUN iajs-2566 22 68 , , PUNCT iajs-2566 22 69 Ξ΄ Ξ΄ NOUN iajs-2566 22 70 ) ) PUNCT iajs-2566 22 71 ) ) PUNCT iajs-2566 23 1 βŠ† βŠ† NUM iajs-2566 23 2 b𝑝(f𝛼0 b𝑝(f𝛼0 NOUN iajs-2566 23 3 , , PUNCT iajs-2566 23 4 Ο΅ Ο΅ NOUN iajs-2566 23 5 ) ) PUNCT iajs-2566 23 6 . . PUNCT iajs-2566 24 1 ( ( PUNCT iajs-2566 24 2 see see VERB iajs-2566 24 3 [ [ X iajs-2566 24 4 10 10 NUM iajs-2566 24 5 ] ] SYM iajs-2566 24 6 ) ) PUNCT iajs-2566 24 7 if if SCONJ iajs-2566 24 8 p p NOUN iajs-2566 24 9 is be AUX iajs-2566 24 10 a a DET iajs-2566 24 11 partial partial ADJ iajs-2566 24 12 metric metric ADJ iajs-2566 24 13 space space NOUN iajs-2566 24 14 , , PUNCT iajs-2566 24 15 then then ADV iajs-2566 24 16 the the DET iajs-2566 24 17 function function NOUN iajs-2566 24 18 𝑝𝑠 𝑝𝑠 NUM iajs-2566 24 19 : : PUNCT iajs-2566 24 20 π‘Œ2 π‘Œ2 NOUN iajs-2566 24 21 β†’ β†’ SYM iajs-2566 24 22 𝑅+ 𝑅+ PROPN iajs-2566 24 23 defined define VERB iajs-2566 24 24 by by ADP iajs-2566 24 25 𝑝𝑠(𝛼 𝑝𝑠(𝛼 X iajs-2566 24 26 , , PUNCT iajs-2566 24 27 𝛽 𝛽 NOUN iajs-2566 24 28 ) ) PUNCT iajs-2566 24 29 = = SYM iajs-2566 24 30 2𝑝(𝛼 2𝑝(𝛼 NUM iajs-2566 24 31 , , PUNCT iajs-2566 24 32 𝛽 𝛽 NOUN iajs-2566 24 33 ) ) PUNCT iajs-2566 24 34 – – PUNCT iajs-2566 24 35 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 24 36 , , PUNCT iajs-2566 24 37 𝛼 𝛼 NOUN iajs-2566 24 38 ) ) PUNCT iajs-2566 24 39 – – PUNCT iajs-2566 24 40 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 24 41 , , PUNCT iajs-2566 24 42 𝛽 𝛽 NOUN iajs-2566 24 43 ) ) PUNCT iajs-2566 24 44 is be AUX iajs-2566 24 45 a a DET iajs-2566 24 46 metric metric NOUN iajs-2566 24 47 on on ADP iajs-2566 24 48 y y PROPN iajs-2566 24 49 ( ( PUNCT iajs-2566 24 50 see see VERB iajs-2566 24 51 [ [ X iajs-2566 24 52 6 6 NUM iajs-2566 24 53 ] ] SYM iajs-2566 24 54 ) ) PUNCT iajs-2566 24 55 not not PART iajs-2566 24 56 that that PRON iajs-2566 24 57 , , PUNCT iajs-2566 24 58 the the DET iajs-2566 24 59 sequence sequence NOUN iajs-2566 24 60 { { PUNCT iajs-2566 24 61 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 24 62 } } PUNCT iajs-2566 24 63 is be AUX iajs-2566 24 64 a a DET iajs-2566 24 65 cauchy cauchy ADJ iajs-2566 24 66 sequence sequence NOUN iajs-2566 24 67 in in ADP iajs-2566 24 68 a a DET iajs-2566 24 69 partial partial ADJ iajs-2566 24 70 metric metric ADJ iajs-2566 24 71 space(π‘Œ space(π‘Œ NOUN iajs-2566 24 72 , , PUNCT iajs-2566 24 73 𝑝 𝑝 NOUN iajs-2566 24 74 ) ) PUNCT iajs-2566 24 75 if if SCONJ iajs-2566 24 76 and and CCONJ iajs-2566 24 77 only only ADV iajs-2566 24 78 if if SCONJ iajs-2566 24 79 { { PUNCT iajs-2566 24 80 𝛼n 𝛼n NOUN iajs-2566 24 81 } } PUNCT iajs-2566 24 82 is be AUX iajs-2566 24 83 a a DET iajs-2566 24 84 cauchy cauchy ADJ iajs-2566 24 85 sequence sequence NOUN iajs-2566 24 86 in in ADP iajs-2566 24 87 the the DET iajs-2566 24 88 metric metric ADJ iajs-2566 24 89 space(π‘Œ space(π‘Œ NOUN iajs-2566 24 90 , , PUNCT iajs-2566 24 91 𝑝𝑠 𝑝𝑠 CCONJ iajs-2566 24 92 ) ) PUNCT iajs-2566 24 93 . . PUNCT iajs-2566 25 1 ( ( PUNCT iajs-2566 25 2 see see VERB iajs-2566 25 3 [ [ X iajs-2566 25 4 9 9 NUM iajs-2566 25 5 ] ] PUNCT iajs-2566 25 6 , , PUNCT iajs-2566 25 7 [ [ X iajs-2566 25 8 10 10 NUM iajs-2566 25 9 ] ] PUNCT iajs-2566 25 10 ) ) PUNCT iajs-2566 25 11 a a DET iajs-2566 25 12 partial partial ADJ iajs-2566 25 13 metric metric ADJ iajs-2566 25 14 space space NOUN iajs-2566 25 15 ( ( PUNCT iajs-2566 25 16 π‘Œ π‘Œ PROPN iajs-2566 25 17 , , PUNCT iajs-2566 25 18 𝑝 𝑝 NOUN iajs-2566 25 19 ) ) PUNCT iajs-2566 25 20 is be AUX iajs-2566 25 21 said say VERB iajs-2566 25 22 complete complete ADJ iajs-2566 25 23 if if SCONJ iajs-2566 25 24 and and CCONJ iajs-2566 25 25 only only ADV iajs-2566 25 26 if if SCONJ iajs-2566 25 27 the the DET iajs-2566 25 28 metric metric ADJ iajs-2566 25 29 space space NOUN iajs-2566 25 30 ( ( PUNCT iajs-2566 25 31 π‘Œ π‘Œ PROPN iajs-2566 25 32 , , PUNCT iajs-2566 25 33 𝑝𝑠 𝑝𝑠 CCONJ iajs-2566 25 34 ) ) PUNCT iajs-2566 25 35 is be AUX iajs-2566 25 36 complete complete ADJ iajs-2566 25 37 . . PUNCT iajs-2566 26 1 furthermore furthermore ADV iajs-2566 26 2 , , PUNCT iajs-2566 26 3 limnβ†’βˆž limnβ†’βˆž PROPN iajs-2566 26 4 p𝑠(𝛼𝑛 p𝑠(𝛼𝑛 NOUN iajs-2566 26 5 , , PUNCT iajs-2566 26 6 𝛼 𝛼 NOUN iajs-2566 26 7 ) ) PUNCT iajs-2566 26 8 = = SYM iajs-2566 26 9 0 0 PUNCT iajs-2566 27 1 if if SCONJ iajs-2566 27 2 and and CCONJ iajs-2566 27 3 only only ADV iajs-2566 27 4 if if SCONJ iajs-2566 27 5 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 27 6 , , PUNCT iajs-2566 27 7 𝛼 𝛼 NOUN iajs-2566 27 8 ) ) PUNCT iajs-2566 27 9 = = SYM iajs-2566 27 10 π‘™π‘–π‘šπ‘›β†’βˆžπ‘(𝛼𝑛 π‘™π‘–π‘šπ‘›β†’βˆžπ‘(𝛼𝑛 NOUN iajs-2566 27 11 , , PUNCT iajs-2566 27 12 𝛼 𝛼 NOUN iajs-2566 27 13 ) ) PUNCT iajs-2566 27 14 = = SYM iajs-2566 27 15 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 27 16 , , PUNCT iajs-2566 27 17 π‘š π‘š PROPN iajs-2566 27 18 β†’βˆžπ‘(𝛼𝑛 β†’βˆžπ‘(𝛼𝑛 NUM iajs-2566 27 19 , , PUNCT iajs-2566 27 20 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 27 21 ) ) PUNCT iajs-2566 27 22 . . PUNCT iajs-2566 28 1 ( ( PUNCT iajs-2566 28 2 𝑠𝑒𝑒[9 𝑠𝑒𝑒[9 X iajs-2566 28 3 ] ] PUNCT iajs-2566 28 4 , , PUNCT iajs-2566 28 5 [ [ X iajs-2566 28 6 10 10 NUM iajs-2566 28 7 ] ] SYM iajs-2566 28 8 ) ) PUNCT iajs-2566 28 9 second second ADJ iajs-2566 28 10 , , PUNCT iajs-2566 28 11 we we PRON iajs-2566 28 12 recall recall VERB iajs-2566 28 13 definition definition NOUN iajs-2566 28 14 of of ADP iajs-2566 28 15 d d ADJ iajs-2566 28 16 - - ADJ iajs-2566 28 17 metric metric ADJ iajs-2566 28 18 space space NOUN iajs-2566 28 19 that that PRON iajs-2566 28 20 can can AUX iajs-2566 28 21 be be AUX iajs-2566 28 22 found find VERB iajs-2566 28 23 in in ADP iajs-2566 28 24 [ [ X iajs-2566 28 25 11 11 NUM iajs-2566 28 26 ] ] PUNCT iajs-2566 28 27 , , PUNCT iajs-2566 28 28 [ [ X iajs-2566 28 29 12 12 NUM iajs-2566 28 30 ] ] PUNCT iajs-2566 28 31 , , PUNCT iajs-2566 28 32 [ [ X iajs-2566 28 33 13 13 NUM iajs-2566 28 34 ] ] PUNCT iajs-2566 28 35 a a DET iajs-2566 28 36 non non ADJ iajs-2566 28 37 - - ADJ iajs-2566 28 38 empty empty ADJ iajs-2566 28 39 set set NOUN iajs-2566 28 40 y y PROPN iajs-2566 28 41 is be AUX iajs-2566 28 42 said say VERB iajs-2566 28 43 to to PART iajs-2566 28 44 be be AUX iajs-2566 28 45 d d ADJ iajs-2566 28 46 - - ADJ iajs-2566 28 47 metric metric ADJ iajs-2566 28 48 space space NOUN iajs-2566 28 49 if if SCONJ iajs-2566 28 50 there there PRON iajs-2566 28 51 exists exist VERB iajs-2566 28 52 a a DET iajs-2566 28 53 function function NOUN iajs-2566 28 54 𝐷 𝐷 NOUN iajs-2566 28 55 : : PUNCT iajs-2566 28 56 π‘Œ3 π‘Œ3 PROPN iajs-2566 29 1 β†’ β†’ PUNCT iajs-2566 29 2 [ [ X iajs-2566 29 3 0 0 NUM iajs-2566 29 4 , , PUNCT iajs-2566 29 5 ∞ ∞ PROPN iajs-2566 29 6 ) ) PUNCT iajs-2566 29 7 satisfies satisfy VERB iajs-2566 29 8 the the DET iajs-2566 29 9 following follow VERB iajs-2566 29 10 conditions condition NOUN iajs-2566 29 11 : : PUNCT iajs-2566 29 12 d1 d1 NOUN iajs-2566 29 13 . . PUNCT iajs-2566 30 1 𝐷(𝛼 𝐷(𝛼 NOUN iajs-2566 30 2 , , PUNCT iajs-2566 30 3 𝛽 𝛽 NOUN iajs-2566 30 4 , , PUNCT iajs-2566 30 5 𝛾 𝛾 NOUN iajs-2566 30 6 ) ) PUNCT iajs-2566 30 7 = = SYM iajs-2566 30 8 0 0 NUM iajs-2566 31 1 ⇔ ⇔ X iajs-2566 31 2 𝛼 𝛼 PROPN iajs-2566 31 3 = = SYM iajs-2566 31 4 𝛽 𝛽 PROPN iajs-2566 31 5 = = SYM iajs-2566 31 6 𝛾 𝛾 PROPN iajs-2566 31 7 d2 d2 PROPN iajs-2566 31 8 . . PUNCT iajs-2566 32 1 𝐷(𝛼 𝐷(𝛼 PROPN iajs-2566 32 2 , , PUNCT iajs-2566 32 3 𝛽 𝛽 NOUN iajs-2566 32 4 , , PUNCT iajs-2566 32 5 𝛾 𝛾 NOUN iajs-2566 32 6 ) ) PUNCT iajs-2566 32 7 = = SYM iajs-2566 33 1 𝐷(𝛽 𝐷(𝛽 NOUN iajs-2566 33 2 , , PUNCT iajs-2566 33 3 𝛼 𝛼 NOUN iajs-2566 33 4 , , PUNCT iajs-2566 33 5 𝛾 𝛾 NOUN iajs-2566 33 6 ) ) PUNCT iajs-2566 33 7 = = SYM iajs-2566 34 1 𝐷(𝛾 𝐷(𝛾 NOUN iajs-2566 34 2 , , PUNCT iajs-2566 34 3 𝛼 𝛼 X iajs-2566 34 4 , , PUNCT iajs-2566 34 5 𝛽 𝛽 NOUN iajs-2566 34 6 ) ) PUNCT iajs-2566 34 7 = = SYM iajs-2566 34 8 𝐷 𝐷 PROPN iajs-2566 34 9 ( ( PUNCT iajs-2566 34 10 𝛽 𝛽 NOUN iajs-2566 34 11 , , PUNCT iajs-2566 34 12 𝛾 𝛾 PROPN iajs-2566 34 13 , , PUNCT iajs-2566 34 14 𝛼 𝛼 NOUN iajs-2566 34 15 ) ) PUNCT iajs-2566 34 16 = = SYM iajs-2566 34 17 … … PUNCT iajs-2566 34 18 ( ( PUNCT iajs-2566 34 19 π‘†π›½π‘šπ‘šπ‘’π‘‘π‘Ÿπ›½ π‘†π›½π‘šπ‘šπ‘’π‘‘π‘Ÿπ›½ PROPN iajs-2566 34 20 ) ) PUNCT iajs-2566 34 21 d3 d3 PROPN iajs-2566 34 22 . . PUNCT iajs-2566 35 1 𝐷(𝛼 𝐷(𝛼 NOUN iajs-2566 35 2 , , PUNCT iajs-2566 35 3 𝛽 𝛽 NOUN iajs-2566 35 4 , , PUNCT iajs-2566 35 5 𝛾 𝛾 NOUN iajs-2566 35 6 ) ) PUNCT iajs-2566 35 7 ≀ ≀ NOUN iajs-2566 35 8 𝐷(πœ‡ 𝐷(πœ‡ PUNCT iajs-2566 35 9 , , PUNCT iajs-2566 35 10 𝛽 𝛽 NOUN iajs-2566 35 11 , , PUNCT iajs-2566 35 12 𝛾 𝛾 NOUN iajs-2566 35 13 ) ) PUNCT iajs-2566 36 1 + + X iajs-2566 36 2 𝐷(𝛼 𝐷(𝛼 CCONJ iajs-2566 36 3 , , PUNCT iajs-2566 36 4 πœ‡ πœ‡ X iajs-2566 36 5 , , PUNCT iajs-2566 36 6 𝛾 𝛾 NOUN iajs-2566 36 7 ) ) PUNCT iajs-2566 37 1 + + X iajs-2566 37 2 𝐷(𝛼 𝐷(𝛼 X iajs-2566 37 3 , , PUNCT iajs-2566 37 4 𝛽 𝛽 NOUN iajs-2566 37 5 , , PUNCT iajs-2566 37 6 πœ‡ πœ‡ NOUN iajs-2566 37 7 ) ) PUNCT iajs-2566 37 8 βˆ€Ξ± βˆ€Ξ± NOUN iajs-2566 37 9 , , PUNCT iajs-2566 37 10 Ξ² Ξ² X iajs-2566 37 11 , , PUNCT iajs-2566 37 12 Ξ³ Ξ³ X iajs-2566 37 13 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 37 14 πœ‡ πœ‡ ADP iajs-2566 37 15 ∈ ∈ PROPN iajs-2566 37 16 π‘Œ π‘Œ PROPN iajs-2566 37 17 , , PUNCT iajs-2566 37 18 where where SCONJ iajs-2566 37 19 d d NOUN iajs-2566 37 20 is be AUX iajs-2566 37 21 d d NOUN iajs-2566 37 22 - - ADJ iajs-2566 37 23 metric metric ADJ iajs-2566 37 24 on on ADP iajs-2566 37 25 π‘Œ π‘Œ PROPN iajs-2566 37 26 . . PUNCT iajs-2566 38 1 y y PROPN iajs-2566 38 2 if if SCONJ iajs-2566 38 3 for for ADP iajs-2566 38 4 givenπœ– givenπœ– NOUN iajs-2566 38 5 > > X iajs-2566 38 6 0 0 PROPN iajs-2566 38 7 , , PUNCT iajs-2566 38 8 a a DET iajs-2566 38 9 sequence sequence NOUN iajs-2566 38 10 { { PUNCT iajs-2566 38 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 38 12 } } PUNCT iajs-2566 38 13 in in ADP iajs-2566 38 14 d d ADJ iajs-2566 38 15 - - ADJ iajs-2566 38 16 metric metric ADJ iajs-2566 38 17 space space NOUN iajs-2566 38 18 ( ( PUNCT iajs-2566 38 19 π‘Œ π‘Œ PROPN iajs-2566 38 20 , , PUNCT iajs-2566 38 21 𝐷 𝐷 PROPN iajs-2566 38 22 ) ) PUNCT iajs-2566 38 23 is be AUX iajs-2566 38 24 said say VERB iajs-2566 38 25 converge converge NOUN iajs-2566 38 26 to to ADP iajs-2566 38 27 π›Όβˆˆ π›Όβˆˆ PROPN iajs-2566 38 28 there there PRON iajs-2566 38 29 exists exist VERB iajs-2566 38 30 a a DET iajs-2566 38 31 positive positive ADJ iajs-2566 38 32 integer integer NOUN iajs-2566 38 33 π”ͺ0 π”ͺ0 NOUN iajs-2566 38 34 such such ADJ iajs-2566 38 35 that𝐷(𝛼𝑛 that𝐷(𝛼𝑛 PROPN iajs-2566 38 36 , , PUNCT iajs-2566 38 37 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 38 38 , , PUNCT iajs-2566 38 39 𝛼 𝛼 NOUN iajs-2566 38 40 ) ) PUNCT iajs-2566 38 41 < < X iajs-2566 38 42 πœ– πœ– X iajs-2566 38 43 βˆ€ βˆ€ X iajs-2566 38 44 π‘š π‘š ADP iajs-2566 38 45 β‰₯ β‰₯ NUM iajs-2566 38 46 π”ͺ π”ͺ NOUN iajs-2566 38 47 0 0 NUM iajs-2566 38 48 , , PUNCT iajs-2566 38 49 𝑛 𝑛 PRON iajs-2566 38 50 β‰₯ β‰₯ NOUN iajs-2566 38 51 π”ͺ0 π”ͺ0 ADJ iajs-2566 38 52 . . PUNCT iajs-2566 39 1 [ [ X iajs-2566 39 2 13 13 NUM iajs-2566 39 3 ] ] PUNCT iajs-2566 39 4 a a DET iajs-2566 39 5 sequence sequence NOUN iajs-2566 39 6 { { PUNCT iajs-2566 39 7 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 39 8 } } PUNCT iajs-2566 39 9 in in ADP iajs-2566 39 10 d d ADJ iajs-2566 39 11 - - ADJ iajs-2566 39 12 metric metric ADJ iajs-2566 39 13 space space NOUN iajs-2566 39 14 ( ( PUNCT iajs-2566 39 15 π‘Œ π‘Œ PROPN iajs-2566 39 16 , , PUNCT iajs-2566 39 17 𝐷 𝐷 PROPN iajs-2566 39 18 ) ) PUNCT iajs-2566 39 19 is be AUX iajs-2566 39 20 said say VERB iajs-2566 39 21 cauchy cauchy PROPN iajs-2566 39 22 if if SCONJ iajs-2566 39 23 for for ADP iajs-2566 39 24 given give VERB iajs-2566 39 25 πœ– πœ– PROPN iajs-2566 39 26 > > X iajs-2566 39 27 0 0 NUM iajs-2566 39 28 ; ; PUNCT iajs-2566 39 29 there there PRON iajs-2566 39 30 exists exist VERB iajs-2566 39 31 an an DET iajs-2566 39 32 positive positive ADJ iajs-2566 39 33 integer integer NOUN iajs-2566 39 34 π”ͺ0 π”ͺ0 NOUN iajs-2566 39 35 such such ADJ iajs-2566 39 36 that that DET iajs-2566 39 37 d(𝛼𝑛 d(𝛼𝑛 PROPN iajs-2566 39 38 , , PUNCT iajs-2566 39 39 π›Όπ‘š π›Όπ‘š AUX iajs-2566 39 40 , , PUNCT iajs-2566 39 41 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 39 42 ) ) PUNCT iajs-2566 39 43 < < X iajs-2566 40 1 Ο΅ Ο΅ X iajs-2566 40 2 βˆ€m βˆ€m PROPN iajs-2566 40 3 β‰₯ β‰₯ NUM iajs-2566 40 4 π”ͺ0 π”ͺ0 ADJ iajs-2566 40 5 , , PUNCT iajs-2566 40 6 n n PRON iajs-2566 40 7 β‰₯ β‰₯ NOUN iajs-2566 40 8 π”ͺ0 π”ͺ0 ADJ iajs-2566 40 9 , , PUNCT iajs-2566 40 10 l l X iajs-2566 40 11 β‰₯ β‰₯ NOUN iajs-2566 41 1 π”ͺ0.[13 π”ͺ0.[13 NOUN iajs-2566 41 2 ] ] PUNCT iajs-2566 41 3 a a DET iajs-2566 41 4 sequence sequence NOUN iajs-2566 41 5 { { PUNCT iajs-2566 41 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 41 7 } } PUNCT iajs-2566 41 8 in in ADP iajs-2566 41 9 d d ADJ iajs-2566 41 10 - - ADJ iajs-2566 41 11 metric metric ADJ iajs-2566 41 12 space space NOUN iajs-2566 41 13 ( ( PUNCT iajs-2566 41 14 π‘Œ π‘Œ PROPN iajs-2566 41 15 , , PUNCT iajs-2566 41 16 𝐷 𝐷 PROPN iajs-2566 41 17 ) ) PUNCT iajs-2566 41 18 is be AUX iajs-2566 41 19 said say VERB iajs-2566 41 20 to to PART iajs-2566 41 21 be be AUX iajs-2566 41 22 complete complete ADJ iajs-2566 41 23 if if SCONJ iajs-2566 41 24 every every DET iajs-2566 41 25 cauchy cauchy ADJ iajs-2566 41 26 sequence sequence NOUN iajs-2566 41 27 in in ADP iajs-2566 41 28 y y PROPN iajs-2566 41 29 converges converge VERB iajs-2566 41 30 to to ADP iajs-2566 41 31 a a DET iajs-2566 41 32 point point NOUN iajs-2566 41 33 𝛼 𝛼 NOUN iajs-2566 41 34 in in ADP iajs-2566 41 35 y. y. PROPN iajs-2566 41 36 a a DET iajs-2566 41 37 sequence sequence NOUN iajs-2566 41 38 { { PUNCT iajs-2566 41 39 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 41 40 } } PUNCT iajs-2566 41 41 in in ADP iajs-2566 41 42 d d ADJ iajs-2566 41 43 - - ADJ iajs-2566 41 44 metric metric ADJ iajs-2566 41 45 space space NOUN iajs-2566 41 46 ( ( PUNCT iajs-2566 41 47 π‘Œ π‘Œ PROPN iajs-2566 41 48 , , PUNCT iajs-2566 41 49 𝐷 𝐷 NOUN iajs-2566 41 50 ) ) PUNCT iajs-2566 41 51 converges converge VERB iajs-2566 41 52 strongly strongly ADV iajs-2566 41 53 to to ADP iajs-2566 41 54 an an DET iajs-2566 41 55 element element NOUN iajs-2566 41 56 𝛼 𝛼 NOUN iajs-2566 41 57 in in ADP iajs-2566 41 58 y y PRON iajs-2566 41 59 if if SCONJ iajs-2566 41 60 ( ( PUNCT iajs-2566 41 61 𝑖)𝐷(𝛼𝑛 𝑖)𝐷(𝛼𝑛 PROPN iajs-2566 41 62 , , PUNCT iajs-2566 41 63 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 41 64 , , PUNCT iajs-2566 41 65 𝛼 𝛼 NOUN iajs-2566 41 66 ) ) PUNCT iajs-2566 41 67 β†’ β†’ SYM iajs-2566 41 68 0 0 NUM iajs-2566 41 69 π‘Žπ‘  π‘Žπ‘  PROPN iajs-2566 41 70 𝑛 𝑛 PROPN iajs-2566 41 71 , , PUNCT iajs-2566 41 72 π‘š π‘š PROPN iajs-2566 41 73 β†’ β†’ SYM iajs-2566 41 74 ∞. ∞. PROPN iajs-2566 41 75 ( ( PUNCT iajs-2566 41 76 𝑖𝑖 𝑖𝑖 NOUN iajs-2566 41 77 ) ) PUNCT iajs-2566 41 78 { { PUNCT iajs-2566 41 79 𝐷(𝛽 𝐷(𝛽 NOUN iajs-2566 41 80 , , PUNCT iajs-2566 41 81 𝛽 𝛽 PROPN iajs-2566 41 82 , , PUNCT iajs-2566 41 83 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 41 84 ) ) PUNCT iajs-2566 41 85 } } PUNCT iajs-2566 41 86 converges converge VERB iajs-2566 41 87 to to ADP iajs-2566 41 88 𝐷(𝛽 𝐷(𝛽 SYM iajs-2566 41 89 , , PUNCT iajs-2566 41 90 𝛽 𝛽 NOUN iajs-2566 41 91 , , PUNCT iajs-2566 41 92 𝛼 𝛼 NOUN iajs-2566 41 93 ) ) PUNCT iajs-2566 41 94 βˆ€ βˆ€ PUNCT iajs-2566 41 95 𝛽 𝛽 NOUN iajs-2566 41 96 ∈ ∈ X iajs-2566 41 97 π‘Œ. π‘Œ. PROPN iajs-2566 42 1 [ [ X iajs-2566 42 2 13 13 NUM iajs-2566 42 3 ] ] PUNCT iajs-2566 42 4 a a DET iajs-2566 42 5 sequence sequence NOUN iajs-2566 42 6 { { PUNCT iajs-2566 42 7 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 42 8 } } PUNCT iajs-2566 42 9 in in ADP iajs-2566 42 10 d d ADJ iajs-2566 42 11 - - ADJ iajs-2566 42 12 metric metric ADJ iajs-2566 42 13 space space NOUN iajs-2566 42 14 ( ( PUNCT iajs-2566 42 15 π‘Œ π‘Œ PROPN iajs-2566 42 16 , , PUNCT iajs-2566 42 17 𝐷 𝐷 PROPN iajs-2566 42 18 ) ) PUNCT iajs-2566 42 19 is be AUX iajs-2566 42 20 said say VERB iajs-2566 42 21 to to PART iajs-2566 42 22 be be AUX iajs-2566 42 23 very very ADV iajs-2566 42 24 strongly strongly ADV iajs-2566 42 25 converges converge NOUN iajs-2566 42 26 to to ADP iajs-2566 42 27 an an DET iajs-2566 42 28 element element NOUN iajs-2566 42 29 𝛼 𝛼 NOUN iajs-2566 42 30 in in ADP iajs-2566 42 31 y y PROPN iajs-2566 42 32 if if SCONJ iajs-2566 42 33 49 49 NUM iajs-2566 42 34 ibn ibn PROPN iajs-2566 42 35 al al PROPN iajs-2566 42 36 - - PUNCT iajs-2566 42 37 haitham haitham PROPN iajs-2566 42 38 jour jour X iajs-2566 42 39 . . PROPN iajs-2566 43 1 for for ADP iajs-2566 43 2 pure pure ADJ iajs-2566 43 3 & & CCONJ iajs-2566 43 4 appl appl PROPN iajs-2566 43 5 . . PUNCT iajs-2566 44 1 sci sci PROPN iajs-2566 44 2 . . PROPN iajs-2566 45 1 34 34 NUM iajs-2566 45 2 ( ( PUNCT iajs-2566 45 3 1 1 NUM iajs-2566 45 4 ) ) PUNCT iajs-2566 45 5 2021 2021 NUM iajs-2566 45 6 ( ( PUNCT iajs-2566 45 7 𝑖)𝐷(𝛼𝑛 𝑖)𝐷(𝛼𝑛 PROPN iajs-2566 45 8 , , PUNCT iajs-2566 45 9 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 45 10 , , PUNCT iajs-2566 45 11 𝛼 𝛼 NOUN iajs-2566 45 12 ) ) PUNCT iajs-2566 45 13 β†’ β†’ SYM iajs-2566 45 14 0 0 NUM iajs-2566 45 15 π‘Žπ‘  π‘Žπ‘  PROPN iajs-2566 45 16 𝑛 𝑛 PROPN iajs-2566 45 17 , , PUNCT iajs-2566 45 18 π‘š π‘š PROPN iajs-2566 45 19 β†’ β†’ SYM iajs-2566 45 20 ∞. ∞. PROPN iajs-2566 45 21 ( ( PUNCT iajs-2566 45 22 𝑖𝑖){𝐷(𝛽 𝑖𝑖){𝐷(𝛽 PROPN iajs-2566 45 23 , , PUNCT iajs-2566 45 24 𝑧 𝑧 PRON iajs-2566 45 25 , , PUNCT iajs-2566 45 26 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 45 27 ) ) PUNCT iajs-2566 45 28 } } PUNCT iajs-2566 45 29 π‘π‘œπ‘›π‘£π‘’π‘Ÿπ‘”π‘’π‘  π‘π‘œπ‘›π‘£π‘’π‘Ÿπ‘”π‘’π‘  VERB iajs-2566 45 30 π‘‘π‘œ π‘‘π‘œ PROPN iajs-2566 45 31 𝐷(𝛽 𝐷(𝛽 NOUN iajs-2566 45 32 , , PUNCT iajs-2566 45 33 𝑧 𝑧 NOUN iajs-2566 45 34 , , PUNCT iajs-2566 45 35 𝛼 𝛼 NOUN iajs-2566 45 36 ) ) PUNCT iajs-2566 45 37 βˆ€π›½ βˆ€π›½ PROPN iajs-2566 45 38 , , PUNCT iajs-2566 45 39 𝑧 𝑧 DET iajs-2566 45 40 ∈ ∈ PROPN iajs-2566 45 41 π‘Œ π‘Œ PROPN iajs-2566 45 42 . . PUNCT iajs-2566 46 1 [ [ X iajs-2566 46 2 13 13 NUM iajs-2566 46 3 ] ] SYM iajs-2566 46 4 2 2 NUM iajs-2566 46 5 . . PUNCT iajs-2566 46 6 generalize generalize VERB iajs-2566 46 7 partial partial ADJ iajs-2566 46 8 metric metric ADJ iajs-2566 46 9 spaces space NOUN iajs-2566 46 10 definition definition NOUN iajs-2566 46 11 1 1 NUM iajs-2566 46 12 a a DET iajs-2566 46 13 non non ADJ iajs-2566 46 14 - - ADJ iajs-2566 46 15 empty empty ADJ iajs-2566 46 16 set set NOUN iajs-2566 46 17 y y PROPN iajs-2566 46 18 is be AUX iajs-2566 46 19 said say VERB iajs-2566 46 20 to to PART iajs-2566 46 21 be be AUX iajs-2566 46 22 a a DET iajs-2566 46 23 general general ADJ iajs-2566 46 24 partial partial ADJ iajs-2566 46 25 metric metric ADJ iajs-2566 46 26 space space NOUN iajs-2566 46 27 if if SCONJ iajs-2566 46 28 there there PRON iajs-2566 46 29 exists exist VERB iajs-2566 46 30 a a DET iajs-2566 46 31 function function NOUN iajs-2566 46 32 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 46 33 : : PUNCT iajs-2566 46 34 π‘Œ3 π‘Œ3 PROPN iajs-2566 47 1 β†’ β†’ PUNCT iajs-2566 47 2 [ [ X iajs-2566 47 3 0 0 NUM iajs-2566 47 4 , , PUNCT iajs-2566 47 5 ∞ ∞ NUM iajs-2566 47 6 ) ) PUNCT iajs-2566 47 7 satisfy satisfy VERB iajs-2566 47 8 the the DET iajs-2566 47 9 following follow VERB iajs-2566 47 10 condition condition NOUN iajs-2566 47 11 : : PUNCT iajs-2566 47 12 dp1 dp1 PROPN iajs-2566 47 13 . . PUNCT iajs-2566 48 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 48 2 , , PUNCT iajs-2566 48 3 𝛼 𝛼 X iajs-2566 48 4 , , PUNCT iajs-2566 48 5 𝛼 𝛼 NOUN iajs-2566 48 6 ) ) PUNCT iajs-2566 48 7 = = SYM iajs-2566 49 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 49 2 ( ( PUNCT iajs-2566 49 3 𝛼 𝛼 PROPN iajs-2566 49 4 , , PUNCT iajs-2566 49 5 𝛽 𝛽 NOUN iajs-2566 49 6 , , PUNCT iajs-2566 49 7 𝛾 𝛾 NOUN iajs-2566 49 8 ) ) PUNCT iajs-2566 49 9 = = SYM iajs-2566 50 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 50 2 ( ( PUNCT iajs-2566 50 3 𝛽 𝛽 PROPN iajs-2566 50 4 , , PUNCT iajs-2566 50 5 𝛽 𝛽 PROPN iajs-2566 50 6 , , PUNCT iajs-2566 50 7 𝛽 𝛽 NOUN iajs-2566 50 8 ) ) PUNCT iajs-2566 50 9 = = SYM iajs-2566 51 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 51 2 , , PUNCT iajs-2566 51 3 𝛾 𝛾 NOUN iajs-2566 51 4 , , PUNCT iajs-2566 51 5 𝛾 𝛾 NOUN iajs-2566 51 6 ) ) PUNCT iajs-2566 51 7 ⇔ ⇔ X iajs-2566 51 8 𝛼 𝛼 PROPN iajs-2566 51 9 = = SYM iajs-2566 51 10 𝛽 𝛽 PROPN iajs-2566 51 11 = = SYM iajs-2566 51 12 𝛾 𝛾 NOUN iajs-2566 51 13 dp2 dp2 NOUN iajs-2566 51 14 . . PUNCT iajs-2566 52 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 52 2 , , PUNCT iajs-2566 52 3 𝛼 𝛼 X iajs-2566 52 4 , , PUNCT iajs-2566 52 5 𝛼 𝛼 NOUN iajs-2566 52 6 ) ) PUNCT iajs-2566 52 7 ≀ ≀ PUNCT iajs-2566 52 8 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 52 9 , , PUNCT iajs-2566 52 10 𝛽 𝛽 NOUN iajs-2566 52 11 , , PUNCT iajs-2566 52 12 𝛾 𝛾 NOUN iajs-2566 52 13 ) ) PUNCT iajs-2566 52 14 dp3 dp3 PROPN iajs-2566 52 15 . . PUNCT iajs-2566 53 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 53 2 , , PUNCT iajs-2566 53 3 𝛽 𝛽 NOUN iajs-2566 53 4 , , PUNCT iajs-2566 53 5 𝛾 𝛾 NOUN iajs-2566 53 6 ) ) PUNCT iajs-2566 53 7 = = SYM iajs-2566 54 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 54 2 ( ( PUNCT iajs-2566 54 3 𝛼 𝛼 PROPN iajs-2566 54 4 , , PUNCT iajs-2566 54 5 𝛾 𝛾 NOUN iajs-2566 54 6 , , PUNCT iajs-2566 54 7 𝛽 𝛽 NOUN iajs-2566 54 8 ) ) PUNCT iajs-2566 54 9 = = SYM iajs-2566 54 10 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 54 11 , , PUNCT iajs-2566 54 12 𝛼 𝛼 X iajs-2566 54 13 , , PUNCT iajs-2566 54 14 𝛾 𝛾 NOUN iajs-2566 54 15 ) ) PUNCT iajs-2566 54 16 = = SYM iajs-2566 55 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 55 2 ( ( PUNCT iajs-2566 55 3 𝛽 𝛽 PROPN iajs-2566 55 4 , , PUNCT iajs-2566 55 5 𝛾 𝛾 PROPN iajs-2566 55 6 , , PUNCT iajs-2566 55 7 𝛼 𝛼 NOUN iajs-2566 55 8 ) ) PUNCT iajs-2566 55 9 = = SYM iajs-2566 55 10 … … PUNCT iajs-2566 55 11 ( ( PUNCT iajs-2566 55 12 π‘†π›½π‘šπ‘šπ‘’π‘‘π‘Ÿπ›½ π‘†π›½π‘šπ‘šπ‘’π‘‘π‘Ÿπ›½ NOUN iajs-2566 55 13 ) ) PUNCT iajs-2566 55 14 dp4 dp4 PROPN iajs-2566 55 15 . . PUNCT iajs-2566 56 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 56 2 , , PUNCT iajs-2566 56 3 𝛽 𝛽 NOUN iajs-2566 56 4 , , PUNCT iajs-2566 56 5 𝛾 𝛾 NOUN iajs-2566 56 6 ) ) PUNCT iajs-2566 56 7 ≀ ≀ NOUN iajs-2566 56 8 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ VERB iajs-2566 56 9 , , PUNCT iajs-2566 56 10 𝛽 𝛽 NOUN iajs-2566 56 11 , , PUNCT iajs-2566 56 12 𝛾 𝛾 NOUN iajs-2566 56 13 ) ) PUNCT iajs-2566 56 14 + + CCONJ iajs-2566 56 15 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 56 16 , , PUNCT iajs-2566 56 17 πœ‡ πœ‡ ADP iajs-2566 56 18 , , PUNCT iajs-2566 56 19 𝛾 𝛾 NOUN iajs-2566 56 20 ) ) PUNCT iajs-2566 56 21 + + CCONJ iajs-2566 57 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 57 2 ( ( PUNCT iajs-2566 57 3 𝛼 𝛼 PROPN iajs-2566 57 4 , , PUNCT iajs-2566 57 5 𝛽 𝛽 NOUN iajs-2566 57 6 , , PUNCT iajs-2566 57 7 πœ‡ πœ‡ ADP iajs-2566 57 8 ) ) PUNCT iajs-2566 57 9 βˆ’ βˆ’ PROPN iajs-2566 57 10 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ PROPN iajs-2566 57 11 , , PUNCT iajs-2566 57 12 πœ‡ πœ‡ ADP iajs-2566 57 13 , , PUNCT iajs-2566 57 14 πœ‡ πœ‡ NOUN iajs-2566 57 15 ) ) PUNCT iajs-2566 57 16 βˆ€ βˆ€ PUNCT iajs-2566 57 17 𝛼 𝛼 NOUN iajs-2566 57 18 , , PUNCT iajs-2566 57 19 𝛽 𝛽 NOUN iajs-2566 57 20 , , PUNCT iajs-2566 57 21 𝛾 𝛾 VERB iajs-2566 57 22 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 57 23 πœ‡ πœ‡ ADP iajs-2566 57 24 ∈ ∈ PROPN iajs-2566 57 25 π‘Œ π‘Œ PROPN iajs-2566 57 26 , , PUNCT iajs-2566 57 27 where where SCONJ iajs-2566 57 28 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 57 29 is be AUX iajs-2566 57 30 general general ADJ iajs-2566 57 31 partial partial ADJ iajs-2566 57 32 metric metric ADJ iajs-2566 57 33 space space NOUN iajs-2566 57 34 on on ADP iajs-2566 57 35 y. y. PROPN iajs-2566 57 36 so so ADV iajs-2566 57 37 , , PUNCT iajs-2566 57 38 given give VERB iajs-2566 57 39 an an DET iajs-2566 57 40 example example NOUN iajs-2566 57 41 of of ADP iajs-2566 57 42 a a DET iajs-2566 57 43 general general ADJ iajs-2566 57 44 partial partial ADJ iajs-2566 57 45 metric metric ADJ iajs-2566 57 46 space space NOUN iajs-2566 57 47 we we PRON iajs-2566 57 48 obtain obtain VERB iajs-2566 57 49 example example NOUN iajs-2566 57 50 2 2 NUM iajs-2566 57 51 let let VERB iajs-2566 57 52 π‘Œ π‘Œ PROPN iajs-2566 57 53 = = PUNCT iajs-2566 58 1 [ [ X iajs-2566 58 2 0 0 NUM iajs-2566 58 3 , , PUNCT iajs-2566 58 4 ∞ ∞ PROPN iajs-2566 58 5 ) ) PUNCT iajs-2566 58 6 and and CCONJ iajs-2566 58 7 define define VERB iajs-2566 58 8 a a DET iajs-2566 58 9 function function NOUN iajs-2566 58 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 58 11 on on ADP iajs-2566 58 12 π‘Œ3 π‘Œ3 PROPN iajs-2566 58 13 by by ADP iajs-2566 58 14 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 58 15 , , PUNCT iajs-2566 58 16 𝛽 𝛽 NOUN iajs-2566 58 17 , , PUNCT iajs-2566 58 18 𝛾 𝛾 NOUN iajs-2566 58 19 ) ) PUNCT iajs-2566 58 20 = = SYM iajs-2566 58 21 π‘šπ‘Žπ›Ό π‘šπ‘Žπ›Ό NOUN iajs-2566 58 22 { { PUNCT iajs-2566 58 23 𝛼 𝛼 NOUN iajs-2566 58 24 , , PUNCT iajs-2566 58 25 𝛽 𝛽 NOUN iajs-2566 58 26 , , PUNCT iajs-2566 58 27 𝛾 𝛾 ADP iajs-2566 58 28 } } PUNCT iajs-2566 58 29 then then ADV iajs-2566 58 30 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 58 31 is be AUX iajs-2566 58 32 a a DET iajs-2566 58 33 general general ADJ iajs-2566 58 34 partial partial ADJ iajs-2566 58 35 metric metric ADJ iajs-2566 58 36 space space NOUN iajs-2566 58 37 on on ADP iajs-2566 58 38 y. y. PROPN iajs-2566 58 39 solution solution NOUN iajs-2566 58 40 : : PUNCT iajs-2566 58 41 1 1 X iajs-2566 58 42 ) ) PUNCT iajs-2566 58 43 since since SCONJ iajs-2566 58 44 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 58 45 , , PUNCT iajs-2566 58 46 𝛽 𝛽 NOUN iajs-2566 58 47 , , PUNCT iajs-2566 58 48 𝛾 𝛾 NOUN iajs-2566 58 49 } } PUNCT iajs-2566 58 50 = = SYM iajs-2566 58 51 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 58 52 , , PUNCT iajs-2566 58 53 𝛼 𝛼 NOUN iajs-2566 58 54 , , PUNCT iajs-2566 58 55 𝛼 𝛼 NOUN iajs-2566 58 56 } } PUNCT iajs-2566 58 57 = = SYM iajs-2566 58 58 π‘šπ‘Žπ›Ό{𝛽 π‘šπ‘Žπ›Ό{𝛽 NOUN iajs-2566 58 59 , , PUNCT iajs-2566 58 60 𝛽 𝛽 PROPN iajs-2566 58 61 , , PUNCT iajs-2566 58 62 𝛽 𝛽 NOUN iajs-2566 58 63 } } PUNCT iajs-2566 58 64 = = ADJ iajs-2566 58 65 π‘šπ‘Žπ›Ό π‘šπ‘Žπ›Ό NOUN iajs-2566 58 66 { { PUNCT iajs-2566 58 67 𝛾 𝛾 NOUN iajs-2566 58 68 , , PUNCT iajs-2566 58 69 𝛾 𝛾 NOUN iajs-2566 58 70 , , PUNCT iajs-2566 58 71 𝛾 𝛾 ADP iajs-2566 58 72 } } PUNCT iajs-2566 58 73 if if SCONJ iajs-2566 58 74 and and CCONJ iajs-2566 58 75 only only ADV iajs-2566 58 76 if if SCONJ iajs-2566 58 77 𝛼 𝛼 X iajs-2566 58 78 = = SYM iajs-2566 58 79 𝛽 𝛽 NOUN iajs-2566 58 80 = = SYM iajs-2566 58 81 𝛾 𝛾 PROPN iajs-2566 58 82 then then ADV iajs-2566 58 83 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PRON iajs-2566 58 84 , , PUNCT iajs-2566 58 85 𝛽 𝛽 NOUN iajs-2566 58 86 , , PUNCT iajs-2566 58 87 𝛾 𝛾 NOUN iajs-2566 58 88 ) ) PUNCT iajs-2566 58 89 = = SYM iajs-2566 59 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 59 2 , , PUNCT iajs-2566 59 3 𝛼 𝛼 X iajs-2566 59 4 , , PUNCT iajs-2566 59 5 𝛼 𝛼 NOUN iajs-2566 59 6 ) ) PUNCT iajs-2566 59 7 = = SYM iajs-2566 59 8 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 59 9 , , PUNCT iajs-2566 59 10 𝛽 𝛽 NOUN iajs-2566 59 11 , , PUNCT iajs-2566 59 12 𝛽 𝛽 NOUN iajs-2566 59 13 ) ) PUNCT iajs-2566 59 14 = = SYM iajs-2566 60 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 60 2 , , PUNCT iajs-2566 60 3 𝛾 𝛾 NOUN iajs-2566 60 4 , , PUNCT iajs-2566 60 5 𝛾 𝛾 NOUN iajs-2566 60 6 ) ) PUNCT iajs-2566 60 7 if if SCONJ iajs-2566 60 8 and and CCONJ iajs-2566 60 9 only only ADV iajs-2566 60 10 if if SCONJ iajs-2566 60 11 𝛼 𝛼 X iajs-2566 60 12 = = SYM iajs-2566 60 13 𝛽 𝛽 NOUN iajs-2566 60 14 = = SYM iajs-2566 60 15 𝛾 𝛾 PROPN iajs-2566 60 16 2 2 NUM iajs-2566 60 17 ) ) PUNCT iajs-2566 60 18 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 60 19 , , PUNCT iajs-2566 60 20 𝛼 𝛼 X iajs-2566 60 21 , , PUNCT iajs-2566 60 22 𝛼 𝛼 NOUN iajs-2566 60 23 ) ) PUNCT iajs-2566 60 24 = = SYM iajs-2566 60 25 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 60 26 , , PUNCT iajs-2566 60 27 𝛼 𝛼 NOUN iajs-2566 60 28 , , PUNCT iajs-2566 60 29 𝛼 𝛼 NOUN iajs-2566 60 30 } } PUNCT iajs-2566 60 31 = = SYM iajs-2566 60 32 𝛼 𝛼 NOUN iajs-2566 60 33 ≀ ≀ NUM iajs-2566 60 34 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 60 35 , , PUNCT iajs-2566 60 36 𝛽 𝛽 NOUN iajs-2566 60 37 , , PUNCT iajs-2566 60 38 𝛾 𝛾 NOUN iajs-2566 60 39 } } PUNCT iajs-2566 60 40 = = SYM iajs-2566 60 41 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 60 42 , , PUNCT iajs-2566 60 43 𝛽 𝛽 NOUN iajs-2566 60 44 , , PUNCT iajs-2566 60 45 𝛾 𝛾 PROPN iajs-2566 60 46 ) ) PUNCT iajs-2566 60 47 . . PUNCT iajs-2566 61 1 3 3 X iajs-2566 61 2 ) ) PUNCT iajs-2566 61 3 trivial trivial ADJ iajs-2566 61 4 4 4 NUM iajs-2566 61 5 ) ) PUNCT iajs-2566 61 6 since since SCONJ iajs-2566 61 7 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 61 8 , , PUNCT iajs-2566 61 9 𝛽 𝛽 NOUN iajs-2566 61 10 , , PUNCT iajs-2566 61 11 𝛾 𝛾 ADP iajs-2566 61 12 } } PUNCT iajs-2566 61 13 ≀ ≀ NUM iajs-2566 61 14 π‘šπ‘Žπ›Ό{πœ‡ π‘šπ‘Žπ›Ό{πœ‡ NOUN iajs-2566 61 15 , , PUNCT iajs-2566 61 16 𝛽 𝛽 NOUN iajs-2566 61 17 , , PUNCT iajs-2566 61 18 𝛾 𝛾 ADP iajs-2566 61 19 } } PUNCT iajs-2566 61 20 + + CCONJ iajs-2566 61 21 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 61 22 , , PUNCT iajs-2566 61 23 πœ‡ πœ‡ ADP iajs-2566 61 24 , , PUNCT iajs-2566 61 25 𝛾 𝛾 ADP iajs-2566 61 26 } } PUNCT iajs-2566 61 27 + + CCONJ iajs-2566 61 28 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 61 29 , , PUNCT iajs-2566 61 30 𝛽 𝛽 NOUN iajs-2566 61 31 , , PUNCT iajs-2566 61 32 πœ‡ πœ‡ ADP iajs-2566 61 33 } } PUNCT iajs-2566 61 34 – – PUNCT iajs-2566 61 35 π‘šπ‘Žπ›Ό{πœ‡ π‘šπ‘Žπ›Ό{πœ‡ NOUN iajs-2566 61 36 , , PUNCT iajs-2566 61 37 πœ‡ πœ‡ X iajs-2566 61 38 , , PUNCT iajs-2566 61 39 πœ‡ πœ‡ ADP iajs-2566 61 40 } } PUNCT iajs-2566 61 41 then then ADV iajs-2566 61 42 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PRON iajs-2566 61 43 , , PUNCT iajs-2566 61 44 𝛽 𝛽 NOUN iajs-2566 61 45 , , PUNCT iajs-2566 61 46 𝛾 𝛾 NOUN iajs-2566 61 47 ) ) PUNCT iajs-2566 61 48 + + CCONJ iajs-2566 61 49 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 61 50 , , PUNCT iajs-2566 61 51 πœ‡ πœ‡ ADP iajs-2566 61 52 , , PUNCT iajs-2566 61 53 πœ‡ πœ‡ ADP iajs-2566 61 54 ) ) PUNCT iajs-2566 61 55 ≀ ≀ NUM iajs-2566 61 56 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ VERB iajs-2566 61 57 , , PUNCT iajs-2566 61 58 𝛽 𝛽 NOUN iajs-2566 61 59 , , PUNCT iajs-2566 61 60 𝛾 𝛾 NOUN iajs-2566 61 61 ) ) PUNCT iajs-2566 61 62 + + CCONJ iajs-2566 61 63 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 61 64 , , PUNCT iajs-2566 61 65 πœ‡ πœ‡ ADP iajs-2566 61 66 , , PUNCT iajs-2566 61 67 𝛾 𝛾 NOUN iajs-2566 61 68 ) ) PUNCT iajs-2566 61 69 + + CCONJ iajs-2566 61 70 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 61 71 , , PUNCT iajs-2566 61 72 𝛽 𝛽 NOUN iajs-2566 61 73 , , PUNCT iajs-2566 61 74 πœ‡ πœ‡ NOUN iajs-2566 61 75 ) ) PUNCT iajs-2566 61 76 βŽ• βŽ• VERB iajs-2566 62 1 definition definition NOUN iajs-2566 62 2 3 3 NUM iajs-2566 62 3 let let VERB iajs-2566 62 4 ( ( PUNCT iajs-2566 62 5 π‘Œ π‘Œ PROPN iajs-2566 62 6 , , PUNCT iajs-2566 62 7 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 62 8 ) ) PUNCT iajs-2566 62 9 be be VERB iajs-2566 62 10 a a DET iajs-2566 62 11 general general ADJ iajs-2566 62 12 partial partial ADJ iajs-2566 62 13 metric metric ADJ iajs-2566 62 14 space space NOUN iajs-2566 62 15 , , PUNCT iajs-2566 62 16 then then ADV iajs-2566 62 17 ( ( PUNCT iajs-2566 62 18 1 1 X iajs-2566 62 19 ) ) PUNCT iajs-2566 62 20 a a DET iajs-2566 62 21 sequence sequence NOUN iajs-2566 62 22 { { PUNCT iajs-2566 62 23 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 62 24 } } PUNCT iajs-2566 62 25 in in ADP iajs-2566 62 26 ( ( PUNCT iajs-2566 62 27 π‘Œ π‘Œ PROPN iajs-2566 62 28 , , PUNCT iajs-2566 62 29 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 62 30 ) ) PUNCT iajs-2566 62 31 converges converge VERB iajs-2566 62 32 to to ADP iajs-2566 62 33 a a DET iajs-2566 62 34 point point NOUN iajs-2566 62 35 𝛼 𝛼 PRON iajs-2566 62 36 ∈ ∈ PROPN iajs-2566 62 37 π‘Œif π‘Œif NOUN iajs-2566 62 38 limn limn NOUN iajs-2566 62 39 , , PUNCT iajs-2566 62 40 m m VERB iajs-2566 62 41 β†’βˆž β†’βˆž PRON iajs-2566 62 42 d𝑝(𝛼𝑛 d𝑝(𝛼𝑛 NOUN iajs-2566 62 43 , , PUNCT iajs-2566 62 44 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 62 45 , , PUNCT iajs-2566 62 46 𝛼 𝛼 NOUN iajs-2566 62 47 ) ) PUNCT iajs-2566 62 48 = = SYM iajs-2566 63 1 d𝑝(𝛼 d𝑝(𝛼 NOUN iajs-2566 63 2 , , PUNCT iajs-2566 63 3 𝛼 𝛼 X iajs-2566 63 4 , , PUNCT iajs-2566 63 5 𝛼 𝛼 NOUN iajs-2566 63 6 ) ) PUNCT iajs-2566 63 7 ( ( PUNCT iajs-2566 63 8 2 2 X iajs-2566 63 9 ) ) PUNCT iajs-2566 63 10 a a DET iajs-2566 63 11 sequence sequence NOUN iajs-2566 63 12 { { PUNCT iajs-2566 63 13 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 63 14 } } PUNCT iajs-2566 63 15 in in ADP iajs-2566 63 16 ( ( PUNCT iajs-2566 63 17 π‘Œ π‘Œ PROPN iajs-2566 63 18 , , PUNCT iajs-2566 63 19 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 63 20 ) ) PUNCT iajs-2566 63 21 is be AUX iajs-2566 63 22 cauchy cauchy ADJ iajs-2566 63 23 sequence sequence NOUN iajs-2566 63 24 if if SCONJ iajs-2566 63 25 limn limn PROPN iajs-2566 63 26 , , PUNCT iajs-2566 63 27 m m VERB iajs-2566 63 28 , , PUNCT iajs-2566 63 29 l l NOUN iajs-2566 63 30 β†’βˆž β†’βˆž X iajs-2566 63 31 d𝑝(𝛼𝑛 d𝑝(𝛼𝑛 NOUN iajs-2566 63 32 , , PUNCT iajs-2566 63 33 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 63 34 , , PUNCT iajs-2566 63 35 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 63 36 ) ) PUNCT iajs-2566 63 37 exists exist VERB iajs-2566 63 38 ( ( PUNCT iajs-2566 63 39 finite finite PROPN iajs-2566 63 40 ) ) PUNCT iajs-2566 63 41 ( ( PUNCT iajs-2566 63 42 3 3 X iajs-2566 63 43 ) ) PUNCT iajs-2566 63 44 a a DET iajs-2566 63 45 general general ADJ iajs-2566 63 46 partial partial ADJ iajs-2566 63 47 metric metric ADJ iajs-2566 63 48 space space NOUN iajs-2566 63 49 ( ( PUNCT iajs-2566 63 50 π‘Œ π‘Œ PROPN iajs-2566 63 51 , , PUNCT iajs-2566 63 52 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 63 53 ) ) PUNCT iajs-2566 63 54 is be AUX iajs-2566 63 55 said say VERB iajs-2566 63 56 to to PART iajs-2566 63 57 be be AUX iajs-2566 63 58 complete complete ADJ iajs-2566 63 59 if if SCONJ iajs-2566 63 60 every every DET iajs-2566 63 61 cauchy cauchy ADJ iajs-2566 63 62 sequence sequence NOUN iajs-2566 63 63 is be AUX iajs-2566 63 64 converge converge ADJ iajs-2566 63 65 to to ADP iajs-2566 63 66 a a DET iajs-2566 63 67 point point NOUN iajs-2566 63 68 𝛼 𝛼 NOUN iajs-2566 63 69 in in ADP iajs-2566 63 70 y. y. PROPN iajs-2566 63 71 ( ( PUNCT iajs-2566 63 72 4 4 NUM iajs-2566 63 73 ) ) PUNCT iajs-2566 63 74 a a DET iajs-2566 63 75 sequence sequence NOUN iajs-2566 63 76 { { PUNCT iajs-2566 63 77 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 63 78 } } PUNCT iajs-2566 63 79 in in ADP iajs-2566 63 80 ( ( PUNCT iajs-2566 63 81 π‘Œ π‘Œ PROPN iajs-2566 63 82 , , PUNCT iajs-2566 63 83 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 63 84 ) ) PUNCT iajs-2566 63 85 is be AUX iajs-2566 63 86 a a DET iajs-2566 63 87 strongly strongly ADV iajs-2566 63 88 converge converge ADJ iajs-2566 63 89 to to ADP iajs-2566 63 90 𝛼 𝛼 PRON iajs-2566 63 91 if if SCONJ iajs-2566 63 92 50 50 NUM iajs-2566 63 93 ibn ibn PROPN iajs-2566 63 94 al al PROPN iajs-2566 63 95 - - PUNCT iajs-2566 63 96 haitham haitham PROPN iajs-2566 63 97 jour jour X iajs-2566 63 98 . . PROPN iajs-2566 64 1 for for ADP iajs-2566 64 2 pure pure ADJ iajs-2566 64 3 & & CCONJ iajs-2566 64 4 appl appl PROPN iajs-2566 64 5 . . PUNCT iajs-2566 65 1 sci sci PROPN iajs-2566 65 2 . . PROPN iajs-2566 66 1 34 34 NUM iajs-2566 66 2 ( ( PUNCT iajs-2566 66 3 1 1 NUM iajs-2566 66 4 ) ) PUNCT iajs-2566 66 5 2021 2021 NUM iajs-2566 66 6 i. i. NOUN iajs-2566 66 7 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 PROPN iajs-2566 66 8 , , PUNCT iajs-2566 66 9 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 66 10 , , PUNCT iajs-2566 66 11 𝛼 𝛼 NOUN iajs-2566 66 12 ) ) PUNCT iajs-2566 66 13 β†’ β†’ SYM iajs-2566 66 14 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 66 15 , , PUNCT iajs-2566 66 16 𝛼 𝛼 INTJ iajs-2566 66 17 , , PUNCT iajs-2566 66 18 𝛼 𝛼 NOUN iajs-2566 66 19 ) ) PUNCT iajs-2566 66 20 π‘Žπ‘  π‘Žπ‘  NOUN iajs-2566 66 21 𝑛 𝑛 PROPN iajs-2566 66 22 , , PUNCT iajs-2566 66 23 π‘š π‘š PROPN iajs-2566 66 24 β†’ β†’ SYM iajs-2566 66 25 ∞ ∞ NUM iajs-2566 66 26 ii ii PROPN iajs-2566 66 27 . . PUNCT iajs-2566 67 1 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 67 2 , , PUNCT iajs-2566 67 3 𝛽 𝛽 NOUN iajs-2566 67 4 , , PUNCT iajs-2566 67 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 67 6 ) ) PUNCT iajs-2566 67 7 β†’ β†’ SYM iajs-2566 67 8 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 67 9 , , PUNCT iajs-2566 67 10 𝛽 𝛽 NOUN iajs-2566 67 11 , , PUNCT iajs-2566 67 12 𝛼 𝛼 PROPN iajs-2566 67 13 ) ) PUNCT iajs-2566 67 14 π‘Žπ‘  π‘Žπ‘  ADP iajs-2566 67 15 𝑛 𝑛 PROPN iajs-2566 67 16 β†’ β†’ SYM iajs-2566 67 17 ∞ ∞ NUM iajs-2566 67 18 βˆ€π›½ βˆ€π›½ PROPN iajs-2566 67 19 ∈ ∈ PROPN iajs-2566 67 20 π‘Œ π‘Œ PROPN iajs-2566 67 21 ( ( PUNCT iajs-2566 67 22 5 5 NUM iajs-2566 67 23 ) ) PUNCT iajs-2566 67 24 a a DET iajs-2566 67 25 sequence sequence NOUN iajs-2566 67 26 { { PUNCT iajs-2566 67 27 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 67 28 } } PUNCT iajs-2566 67 29 in in ADP iajs-2566 67 30 ( ( PUNCT iajs-2566 67 31 π‘Œ π‘Œ PROPN iajs-2566 67 32 , , PUNCT iajs-2566 67 33 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 67 34 ) ) PUNCT iajs-2566 67 35 is be AUX iajs-2566 67 36 a a DET iajs-2566 67 37 very very ADV iajs-2566 67 38 strongly strongly ADV iajs-2566 67 39 converge converge ADJ iajs-2566 67 40 to to ADP iajs-2566 67 41 𝛼 𝛼 PRON iajs-2566 67 42 if if SCONJ iajs-2566 67 43 i. i. PROPN iajs-2566 67 44 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 PROPN iajs-2566 67 45 , , PUNCT iajs-2566 67 46 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 67 47 , , PUNCT iajs-2566 67 48 𝛼 𝛼 NOUN iajs-2566 67 49 ) ) PUNCT iajs-2566 67 50 β†’ β†’ SYM iajs-2566 67 51 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 67 52 , , PUNCT iajs-2566 67 53 𝛼 𝛼 INTJ iajs-2566 67 54 , , PUNCT iajs-2566 67 55 𝛼 𝛼 NOUN iajs-2566 67 56 ) ) PUNCT iajs-2566 67 57 π‘Žπ‘  π‘Žπ‘  NOUN iajs-2566 67 58 𝑛 𝑛 PROPN iajs-2566 67 59 , , PUNCT iajs-2566 67 60 π‘š π‘š PROPN iajs-2566 67 61 β†’ β†’ SYM iajs-2566 67 62 ∞ ∞ NUM iajs-2566 67 63 ii ii PROPN iajs-2566 67 64 . . PUNCT iajs-2566 67 65 𝐷𝑝(𝛽 𝐷𝑝(𝛽 PROPN iajs-2566 67 66 , , PUNCT iajs-2566 67 67 𝛾 𝛾 PROPN iajs-2566 67 68 , , PUNCT iajs-2566 67 69 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 67 70 ) ) PUNCT iajs-2566 67 71 β†’ β†’ SYM iajs-2566 67 72 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 67 73 , , PUNCT iajs-2566 67 74 𝛾 𝛾 NOUN iajs-2566 67 75 , , PUNCT iajs-2566 67 76 𝛼 𝛼 NOUN iajs-2566 67 77 ) ) PUNCT iajs-2566 67 78 π‘Žπ‘  π‘Žπ‘  ADP iajs-2566 67 79 𝑛 𝑛 PROPN iajs-2566 67 80 β†’ β†’ SYM iajs-2566 67 81 ∞ ∞ NUM iajs-2566 67 82 βˆ€ βˆ€ X iajs-2566 67 83 𝛽 𝛽 NOUN iajs-2566 67 84 , , PUNCT iajs-2566 67 85 𝛾 𝛾 PROPN iajs-2566 67 86 ∈ ∈ PROPN iajs-2566 67 87 π‘Œ π‘Œ PROPN iajs-2566 67 88 ( ( PUNCT iajs-2566 67 89 6 6 NUM iajs-2566 67 90 ) ) PUNCT iajs-2566 67 91 for for ADP iajs-2566 67 92 𝛼 𝛼 PROPN iajs-2566 67 93 ∈ ∈ PROPN iajs-2566 67 94 π‘Œ π‘Œ PROPN iajs-2566 67 95 and and CCONJ iajs-2566 67 96 πœ– πœ– X iajs-2566 67 97 > > X iajs-2566 67 98 0 0 PROPN iajs-2566 67 99 , , PUNCT iajs-2566 67 100 the the DET iajs-2566 67 101 open open ADJ iajs-2566 67 102 ball ball NOUN iajs-2566 67 103 of of ADP iajs-2566 67 104 the the DET iajs-2566 67 105 general general ADJ iajs-2566 67 106 partial partial ADJ iajs-2566 67 107 metric metric ADJ iajs-2566 67 108 space space NOUN iajs-2566 67 109 with with ADP iajs-2566 67 110 center center PROPN iajs-2566 67 111 𝛼 𝛼 NOUN iajs-2566 67 112 and and CCONJ iajs-2566 67 113 radius radius PROPN iajs-2566 67 114 πœ– πœ– PROPN iajs-2566 67 115 is be AUX iajs-2566 67 116 𝐡𝐷𝑝 𝐡𝐷𝑝 NOUN iajs-2566 67 117 ( ( PUNCT iajs-2566 67 118 𝛼 𝛼 PROPN iajs-2566 67 119 , , PUNCT iajs-2566 67 120 πœ– πœ– NOUN iajs-2566 67 121 ) ) PUNCT iajs-2566 67 122 = = NOUN iajs-2566 67 123 { { PUNCT iajs-2566 67 124 𝛽 𝛽 NOUN iajs-2566 67 125 ∈ ∈ PROPN iajs-2566 67 126 π‘Œ π‘Œ PROPN iajs-2566 67 127 ∢ ∢ PROPN iajs-2566 67 128 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 67 129 , , PUNCT iajs-2566 67 130 𝛽 𝛽 PROPN iajs-2566 67 131 , , PUNCT iajs-2566 67 132 𝛽 𝛽 PROPN iajs-2566 67 133 ) ) PUNCT iajs-2566 67 134 < < X iajs-2566 68 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 INTJ iajs-2566 68 2 , , PUNCT iajs-2566 68 3 𝛼 𝛼 INTJ iajs-2566 68 4 , , PUNCT iajs-2566 68 5 𝛼 𝛼 PROPN iajs-2566 68 6 ) ) PUNCT iajs-2566 68 7 + + CCONJ iajs-2566 68 8 πœ– πœ– X iajs-2566 68 9 } } PUNCT iajs-2566 68 10 . . PUNCT iajs-2566 69 1 ( ( PUNCT iajs-2566 69 2 7 7 X iajs-2566 69 3 ) ) PUNCT iajs-2566 69 4 a a DET iajs-2566 69 5 mapping mapping NOUN iajs-2566 69 6 𝐹 𝐹 PROPN iajs-2566 69 7 : : PUNCT iajs-2566 69 8 ( ( PUNCT iajs-2566 69 9 π‘Œ π‘Œ PROPN iajs-2566 69 10 , , PUNCT iajs-2566 69 11 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 69 12 ) ) PUNCT iajs-2566 69 13 β†’ β†’ PUNCT iajs-2566 69 14 ( ( PUNCT iajs-2566 69 15 π‘Œ π‘Œ PROPN iajs-2566 69 16 β€² β€² NOUN iajs-2566 69 17 , , PUNCT iajs-2566 69 18 𝐷𝑝′ 𝐷𝑝′ NOUN iajs-2566 69 19 ) ) PUNCT iajs-2566 69 20 is be AUX iajs-2566 69 21 said say VERB iajs-2566 69 22 to to PART iajs-2566 69 23 be be AUX iajs-2566 69 24 continuous continuous ADJ iajs-2566 69 25 at at ADP iajs-2566 69 26 𝛼 𝛼 PRON iajs-2566 69 27 if if SCONJ iajs-2566 69 28 for for ADP iajs-2566 69 29 each each DET iajs-2566 69 30 open open ADJ iajs-2566 69 31 ball ball NOUN iajs-2566 69 32 𝐡𝐷𝑝 𝐡𝐷𝑝 NOUN iajs-2566 69 33 ( ( PUNCT iajs-2566 69 34 𝐹(𝛼 𝐹(𝛼 NUM iajs-2566 69 35 ) ) PUNCT iajs-2566 69 36 , , PUNCT iajs-2566 69 37 πœ–β€² πœ–β€² NOUN iajs-2566 69 38 ) ) PUNCT iajs-2566 69 39 in in ADP iajs-2566 69 40 ( ( PUNCT iajs-2566 69 41 π‘Œβ€² π‘Œβ€² PROPN iajs-2566 69 42 , , PUNCT iajs-2566 69 43 𝐷𝑝′ 𝐷𝑝′ NOUN iajs-2566 69 44 ) ) PUNCT iajs-2566 69 45 there there PRON iajs-2566 69 46 exists exist VERB iajs-2566 69 47 a a DET iajs-2566 69 48 ball ball NOUN iajs-2566 69 49 𝐡𝑝(𝛼 𝐡𝑝(𝛼 ADJ iajs-2566 69 50 , , PUNCT iajs-2566 69 51 πœ– πœ– PROPN iajs-2566 69 52 ) ) PUNCT iajs-2566 69 53 in in ADP iajs-2566 69 54 ( ( PUNCT iajs-2566 69 55 π‘Œ π‘Œ PROPN iajs-2566 69 56 , , PUNCT iajs-2566 69 57 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 69 58 ) ) PUNCT iajs-2566 69 59 such such ADJ iajs-2566 69 60 that that SCONJ iajs-2566 69 61 𝐹(𝐡𝐷𝑝 𝐹(𝐡𝐷𝑝 PROPN iajs-2566 69 62 ( ( PUNCT iajs-2566 69 63 𝛼 𝛼 PROPN iajs-2566 69 64 , , PUNCT iajs-2566 69 65 πœ– πœ– PROPN iajs-2566 69 66 ) ) PUNCT iajs-2566 69 67 ) ) PUNCT iajs-2566 69 68 βŠ† βŠ† NUM iajs-2566 69 69 𝐡𝐷𝑝 𝐡𝐷𝑝 NOUN iajs-2566 69 70 ( ( PUNCT iajs-2566 69 71 𝐹(𝛼 𝐹(𝛼 NUM iajs-2566 69 72 ) ) PUNCT iajs-2566 69 73 , , PUNCT iajs-2566 69 74 πœ–β€² πœ–β€² NOUN iajs-2566 69 75 ) ) PUNCT iajs-2566 69 76 . . PUNCT iajs-2566 70 1 not not PART iajs-2566 70 2 that that SCONJ iajs-2566 70 3 , , PUNCT iajs-2566 70 4 if if SCONJ iajs-2566 70 5 { { PUNCT iajs-2566 70 6 𝛼𝑛 𝛼𝑛 X iajs-2566 70 7 } } PUNCT iajs-2566 70 8 is be AUX iajs-2566 70 9 a a DET iajs-2566 70 10 converge converge NOUN iajs-2566 70 11 sequence sequence NOUN iajs-2566 70 12 in(π‘Œ in(π‘Œ ADJ iajs-2566 70 13 , , PUNCT iajs-2566 70 14 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 70 15 ) ) PUNCT iajs-2566 70 16 then then ADV iajs-2566 70 17 the the DET iajs-2566 70 18 converge converge NOUN iajs-2566 70 19 point point NOUN iajs-2566 70 20 is be AUX iajs-2566 70 21 not not PART iajs-2566 70 22 unique unique ADJ iajs-2566 70 23 . . PUNCT iajs-2566 71 1 example4 example4 NOUN iajs-2566 71 2 let let VERB iajs-2566 71 3 π‘Œ π‘Œ PROPN iajs-2566 71 4 = = PUNCT iajs-2566 72 1 [ [ X iajs-2566 72 2 0 0 NUM iajs-2566 72 3 , , PUNCT iajs-2566 72 4 ∞ ∞ PROPN iajs-2566 72 5 ) ) PUNCT iajs-2566 72 6 with with ADP iajs-2566 72 7 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 72 8 , , PUNCT iajs-2566 72 9 𝛽 𝛽 NOUN iajs-2566 72 10 , , PUNCT iajs-2566 72 11 𝛾 𝛾 NOUN iajs-2566 72 12 ) ) PUNCT iajs-2566 72 13 = = SYM iajs-2566 72 14 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 72 15 , , PUNCT iajs-2566 72 16 𝛽 𝛽 NOUN iajs-2566 72 17 , , PUNCT iajs-2566 72 18 𝛾 𝛾 ADP iajs-2566 72 19 } } PUNCT iajs-2566 72 20 then then ADV iajs-2566 72 21 ( ( PUNCT iajs-2566 72 22 π‘Œ π‘Œ PROPN iajs-2566 72 23 , , PUNCT iajs-2566 72 24 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 72 25 ) ) PUNCT iajs-2566 72 26 is be AUX iajs-2566 72 27 a a DET iajs-2566 72 28 general general ADJ iajs-2566 72 29 partial partial ADJ iajs-2566 72 30 metric metric NOUN iajs-2566 72 31 observe observe VERB iajs-2566 73 1 that that SCONJ iajs-2566 73 2 if if SCONJ iajs-2566 73 3 the the DET iajs-2566 73 4 sequence sequence NOUN iajs-2566 73 5 { { PUNCT iajs-2566 73 6 1 1 NUM iajs-2566 73 7 + + SYM iajs-2566 73 8 1 1 NUM iajs-2566 73 9 𝑛2 𝑛2 NOUN iajs-2566 73 10 } } PUNCT iajs-2566 73 11 , , PUNCT iajs-2566 73 12 𝛼 𝛼 X iajs-2566 73 13 β‰₯ β‰₯ NOUN iajs-2566 73 14 1 1 NUM iajs-2566 73 15 then then ADV iajs-2566 73 16 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 73 17 , , PUNCT iajs-2566 73 18 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 73 19 , , PUNCT iajs-2566 73 20 𝛼 𝛼 NOUN iajs-2566 73 21 ) ) PUNCT iajs-2566 73 22 = = SYM iajs-2566 73 23 π‘™π‘–π‘šπ‘›,π‘šβ†’βˆžπ‘šπ‘Žπ›Ό{1 π‘™π‘–π‘šπ‘›,π‘šβ†’βˆžπ‘šπ‘Žπ›Ό{1 X iajs-2566 73 24 + + CCONJ iajs-2566 73 25 1 1 NUM iajs-2566 73 26 𝑛2 𝑛2 NOUN iajs-2566 73 27 , , PUNCT iajs-2566 73 28 1 1 NUM iajs-2566 73 29 + + SYM iajs-2566 73 30 1 1 NUM iajs-2566 73 31 π‘š2 π‘š2 NOUN iajs-2566 73 32 , , PUNCT iajs-2566 73 33 𝛼 𝛼 NOUN iajs-2566 73 34 } } PUNCT iajs-2566 73 35 = = SYM iajs-2566 73 36 𝛼 𝛼 NOUN iajs-2566 73 37 = = PUNCT iajs-2566 73 38 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 73 39 , , PUNCT iajs-2566 73 40 𝛼 𝛼 INTJ iajs-2566 73 41 , , PUNCT iajs-2566 73 42 𝛼 𝛼 NOUN iajs-2566 73 43 ) ) PUNCT iajs-2566 73 44 . . PUNCT iajs-2566 74 1 hence hence ADV iajs-2566 74 2 , , PUNCT iajs-2566 74 3 every every DET iajs-2566 74 4 𝛼 𝛼 PROPN iajs-2566 74 5 ∈ ∈ NOUN iajs-2566 74 6 [ [ X iajs-2566 74 7 1 1 NUM iajs-2566 74 8 , , PUNCT iajs-2566 74 9 ∞ ∞ PROPN iajs-2566 74 10 ) ) PUNCT iajs-2566 74 11 is be AUX iajs-2566 74 12 a a DET iajs-2566 74 13 convergent convergent NOUN iajs-2566 74 14 point point NOUN iajs-2566 74 15 for for ADP iajs-2566 74 16 the the DET iajs-2566 74 17 sequence sequence NOUN iajs-2566 74 18 { { PUNCT iajs-2566 74 19 1 1 NUM iajs-2566 74 20 + + SYM iajs-2566 74 21 1 1 NUM iajs-2566 74 22 𝑛2 𝑛2 NOUN iajs-2566 74 23 } } PUNCT iajs-2566 74 24 . . PUNCT iajs-2566 75 1 thus thus ADV iajs-2566 75 2 , , PUNCT iajs-2566 75 3 the the DET iajs-2566 75 4 converge converge NOUN iajs-2566 75 5 point point NOUN iajs-2566 75 6 is be AUX iajs-2566 75 7 not not PART iajs-2566 75 8 unique unique ADJ iajs-2566 75 9 . . PUNCT iajs-2566 76 1 theorem theorem VERB iajs-2566 76 2 5 5 NUM iajs-2566 76 3 every every DET iajs-2566 76 4 converge converge NOUN iajs-2566 76 5 sequence sequence NOUN iajs-2566 76 6 in in ADP iajs-2566 76 7 ( ( PUNCT iajs-2566 76 8 π‘Œ π‘Œ PROPN iajs-2566 76 9 , , PUNCT iajs-2566 76 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 76 11 ) ) PUNCT iajs-2566 76 12 is be AUX iajs-2566 76 13 a a DET iajs-2566 76 14 cauchy cauchy ADJ iajs-2566 76 15 sequence sequence NOUN iajs-2566 76 16 . . PUNCT iajs-2566 77 1 proof proof NOUN iajs-2566 77 2 : : PUNCT iajs-2566 77 3 let let VERB iajs-2566 77 4 ( ( PUNCT iajs-2566 77 5 π‘Œ π‘Œ PROPN iajs-2566 77 6 , , PUNCT iajs-2566 77 7 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 77 8 ) ) PUNCT iajs-2566 77 9 be be VERB iajs-2566 77 10 a a DET iajs-2566 77 11 general general ADJ iajs-2566 77 12 partial partial ADJ iajs-2566 77 13 metric metric ADJ iajs-2566 77 14 space space NOUN iajs-2566 77 15 and and CCONJ iajs-2566 77 16 { { PUNCT iajs-2566 77 17 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 77 18 } } PUNCT iajs-2566 77 19 is be AUX iajs-2566 77 20 a a DET iajs-2566 77 21 converge converge NOUN iajs-2566 77 22 sequence sequence NOUN iajs-2566 77 23 to to ADP iajs-2566 77 24 𝛼 𝛼 PRON iajs-2566 77 25 and and CCONJ iajs-2566 77 26 πœ– πœ– X iajs-2566 77 27 > > X iajs-2566 77 28 0 0 NUM iajs-2566 77 29 . . PUNCT iajs-2566 78 1 since since SCONJ iajs-2566 78 2 { { PUNCT iajs-2566 78 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 78 4 } } PUNCT iajs-2566 78 5 is be AUX iajs-2566 78 6 converge converge ADJ iajs-2566 78 7 to to ADP iajs-2566 78 8 𝛼 𝛼 PRON iajs-2566 78 9 then then ADV iajs-2566 78 10 there there PRON iajs-2566 78 11 exists exist VERB iajs-2566 78 12 π‘˜ π‘˜ DET iajs-2566 78 13 ∈ ∈ NOUN iajs-2566 78 14 𝑁 𝑁 ADP iajs-2566 78 15 such such ADJ iajs-2566 78 16 that that DET iajs-2566 78 17 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 NOUN iajs-2566 78 18 , , PUNCT iajs-2566 78 19 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 78 20 , , PUNCT iajs-2566 78 21 𝛼 𝛼 NOUN iajs-2566 78 22 ) ) PUNCT iajs-2566 78 23 – – PUNCT iajs-2566 78 24 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 78 25 , , PUNCT iajs-2566 78 26 𝛼 𝛼 INTJ iajs-2566 78 27 , , PUNCT iajs-2566 78 28 𝛼 𝛼 NOUN iajs-2566 78 29 ) ) PUNCT iajs-2566 79 1 | | ADV iajs-2566 79 2 < < X iajs-2566 79 3 πœ– πœ– X iajs-2566 79 4 βˆ€ βˆ€ X iajs-2566 79 5 𝑛 𝑛 NOUN iajs-2566 79 6 , , PUNCT iajs-2566 79 7 π‘š π‘š X iajs-2566 79 8 > > X iajs-2566 79 9 π‘˜ π‘˜ PRON iajs-2566 80 1 so so ADV iajs-2566 80 2 that that SCONJ iajs-2566 80 3 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 80 4 , , PUNCT iajs-2566 80 5 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 80 6 , , PUNCT iajs-2566 80 7 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 80 8 ) ) PUNCT iajs-2566 80 9 ≀ ≀ NOUN iajs-2566 80 10 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 80 11 , , PUNCT iajs-2566 80 12 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 80 13 , , PUNCT iajs-2566 80 14 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 80 15 ) ) PUNCT iajs-2566 80 16 + + CCONJ iajs-2566 80 17 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 80 18 , , PUNCT iajs-2566 80 19 𝛼 𝛼 NOUN iajs-2566 80 20 , , PUNCT iajs-2566 80 21 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 80 22 ) ) PUNCT iajs-2566 80 23 + + CCONJ iajs-2566 80 24 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 80 25 , , PUNCT iajs-2566 80 26 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 80 27 , , PUNCT iajs-2566 80 28 𝛼 𝛼 NOUN iajs-2566 80 29 ) ) PUNCT iajs-2566 80 30 βˆ’ βˆ’ PROPN iajs-2566 80 31 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 80 32 , , PUNCT iajs-2566 80 33 𝛼 𝛼 X iajs-2566 80 34 , , PUNCT iajs-2566 80 35 𝛼 𝛼 NOUN iajs-2566 80 36 ) ) PUNCT iajs-2566 80 37 ≀ ≀ NOUN iajs-2566 80 38 2𝐷𝑝(𝛼 2𝐷𝑝(𝛼 NUM iajs-2566 80 39 , , PUNCT iajs-2566 80 40 𝛼 𝛼 X iajs-2566 80 41 , , PUNCT iajs-2566 80 42 𝛼 𝛼 NOUN iajs-2566 80 43 ) ) PUNCT iajs-2566 80 44 + + CCONJ iajs-2566 80 45 πœ– πœ– X iajs-2566 80 46 βˆ€ βˆ€ X iajs-2566 80 47 𝑛 𝑛 NOUN iajs-2566 80 48 , , PUNCT iajs-2566 80 49 π‘š π‘š PROPN iajs-2566 80 50 , , PUNCT iajs-2566 80 51 𝑙 𝑙 X iajs-2566 80 52 > > X iajs-2566 80 53 𝐾 𝐾 PROPN iajs-2566 80 54 hence hence ADV iajs-2566 80 55 , , PUNCT iajs-2566 80 56 limn limn PROPN iajs-2566 80 57 , , PUNCT iajs-2566 80 58 m m VERB iajs-2566 80 59 , , PUNCT iajs-2566 80 60 lβ†’βˆž lβ†’βˆž NUM iajs-2566 80 61 d𝑝(𝛼𝑛 d𝑝(𝛼𝑛 NOUN iajs-2566 80 62 , , PUNCT iajs-2566 80 63 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 80 64 , , PUNCT iajs-2566 80 65 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 80 66 ) ) PUNCT iajs-2566 80 67 exists exist VERB iajs-2566 80 68 , , PUNCT iajs-2566 80 69 thus thus ADV iajs-2566 80 70 { { PUNCT iajs-2566 80 71 𝛼𝑛 𝛼𝑛 X iajs-2566 80 72 } } PUNCT iajs-2566 80 73 is be AUX iajs-2566 80 74 a a DET iajs-2566 80 75 cauchy cauchy ADJ iajs-2566 80 76 sequence sequence NOUN iajs-2566 80 77 . . PUNCT iajs-2566 81 1 βŽ• βŽ• PROPN iajs-2566 81 2 remark remark VERB iajs-2566 81 3 6 6 NUM iajs-2566 81 4 it it PRON iajs-2566 81 5 is be AUX iajs-2566 81 6 clear clear ADJ iajs-2566 81 7 from from ADP iajs-2566 81 8 the the DET iajs-2566 81 9 definition definition NOUN iajs-2566 81 10 that that SCONJ iajs-2566 81 11 every every DET iajs-2566 81 12 strong strong ADJ iajs-2566 81 13 converge converge NOUN iajs-2566 81 14 sequence sequence NOUN iajs-2566 81 15 is be AUX iajs-2566 81 16 a a DET iajs-2566 81 17 converge converge NOUN iajs-2566 81 18 but but CCONJ iajs-2566 81 19 the the DET iajs-2566 81 20 opposite opposite NOUN iajs-2566 81 21 is be AUX iajs-2566 81 22 not not PART iajs-2566 81 23 true true ADJ iajs-2566 81 24 , , PUNCT iajs-2566 81 25 as as SCONJ iajs-2566 81 26 we we PRON iajs-2566 81 27 see see VERB iajs-2566 81 28 in in ADP iajs-2566 81 29 example example NOUN iajs-2566 81 30 ( ( PUNCT iajs-2566 81 31 4 4 NUM iajs-2566 81 32 ) ) PUNCT iajs-2566 81 33 that that SCONJ iajs-2566 81 34 a a DET iajs-2566 81 35 sequence sequence NOUN iajs-2566 81 36 { { PUNCT iajs-2566 81 37 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 81 38 } } PUNCT iajs-2566 81 39 = = PUNCT iajs-2566 81 40 { { PUNCT iajs-2566 81 41 1 1 NUM iajs-2566 81 42 + + SYM iajs-2566 81 43 1 1 NUM iajs-2566 81 44 𝑛2 𝑛2 NOUN iajs-2566 81 45 } } PUNCT iajs-2566 81 46 is be AUX iajs-2566 81 47 a a DET iajs-2566 81 48 converge converge NOUN iajs-2566 81 49 to to ADP iajs-2566 81 50 2 2 NUM iajs-2566 81 51 but but CCONJ iajs-2566 81 52 not not PART iajs-2566 81 53 strongly strongly ADV iajs-2566 81 54 a a DET iajs-2566 81 55 converge converge NOUN iajs-2566 81 56 to to ADP iajs-2566 81 57 2 2 NUM iajs-2566 81 58 , , PUNCT iajs-2566 81 59 to to PART iajs-2566 81 60 see see VERB iajs-2566 81 61 this this DET iajs-2566 81 62 51 51 NUM iajs-2566 81 63 ibn ibn PROPN iajs-2566 81 64 al al PROPN iajs-2566 81 65 - - PUNCT iajs-2566 81 66 haitham haitham PROPN iajs-2566 81 67 jour jour X iajs-2566 81 68 . . PROPN iajs-2566 82 1 for for ADP iajs-2566 82 2 pure pure ADJ iajs-2566 82 3 & & CCONJ iajs-2566 82 4 appl appl PROPN iajs-2566 82 5 . . PUNCT iajs-2566 83 1 sci sci PROPN iajs-2566 83 2 . . PROPN iajs-2566 84 1 34 34 NUM iajs-2566 84 2 ( ( PUNCT iajs-2566 84 3 1 1 NUM iajs-2566 84 4 ) ) PUNCT iajs-2566 84 5 2021 2021 NUM iajs-2566 84 6 take take VERB iajs-2566 84 7 1 1 NUM iajs-2566 84 8 < < X iajs-2566 84 9 𝛽 𝛽 NOUN iajs-2566 84 10 < < X iajs-2566 84 11 2 2 NUM iajs-2566 84 12 , , PUNCT iajs-2566 84 13 π‘™π‘–π‘šπ‘›β†’βˆžπ·π‘(𝛽 π‘™π‘–π‘šπ‘›β†’βˆžπ·π‘(𝛽 NOUN iajs-2566 84 14 , , PUNCT iajs-2566 84 15 𝛽 𝛽 PROPN iajs-2566 84 16 , , PUNCT iajs-2566 84 17 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 84 18 ) ) PUNCT iajs-2566 84 19 = = SYM iajs-2566 85 1 𝛽 𝛽 NOUN iajs-2566 85 2 β‰  β‰  ADJ iajs-2566 85 3 2 2 NUM iajs-2566 85 4 = = SYM iajs-2566 85 5 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 85 6 , , PUNCT iajs-2566 85 7 𝛽 𝛽 NOUN iajs-2566 85 8 , , PUNCT iajs-2566 85 9 2 2 NUM iajs-2566 85 10 ) ) PUNCT iajs-2566 85 11 thus thus ADV iajs-2566 85 12 , , PUNCT iajs-2566 85 13 𝛼𝑛 𝛼𝑛 INTJ iajs-2566 85 14 = = SYM iajs-2566 85 15 { { PUNCT iajs-2566 85 16 1 1 NUM iajs-2566 85 17 + + SYM iajs-2566 85 18 1 1 NUM iajs-2566 85 19 𝑛2 𝑛2 NOUN iajs-2566 85 20 } } PUNCT iajs-2566 85 21 is be AUX iajs-2566 85 22 not not PART iajs-2566 85 23 strongly strongly ADV iajs-2566 85 24 converging converge VERB iajs-2566 85 25 to to ADP iajs-2566 85 26 2 2 NUM iajs-2566 85 27 . . PUNCT iajs-2566 85 28 theorem theorem VERB iajs-2566 85 29 7 7 NUM iajs-2566 85 30 if if SCONJ iajs-2566 85 31 { { PUNCT iajs-2566 85 32 𝛼𝑛 𝛼𝑛 X iajs-2566 85 33 } } PUNCT iajs-2566 85 34 is be AUX iajs-2566 85 35 a a DET iajs-2566 85 36 strongly strongly ADV iajs-2566 85 37 converge converge VERB iajs-2566 85 38 , , PUNCT iajs-2566 85 39 then then ADV iajs-2566 85 40 the the DET iajs-2566 85 41 converge converge NOUN iajs-2566 85 42 point point NOUN iajs-2566 85 43 is be AUX iajs-2566 85 44 unique unique ADJ iajs-2566 85 45 . . PUNCT iajs-2566 86 1 proof proof NOUN iajs-2566 86 2 let let VERB iajs-2566 86 3 { { PUNCT iajs-2566 86 4 𝛼𝑛 𝛼𝑛 PART iajs-2566 86 5 } } PUNCT iajs-2566 86 6 be be AUX iajs-2566 86 7 a a DET iajs-2566 86 8 strongly strongly ADV iajs-2566 86 9 converge converge NOUN iajs-2566 86 10 to to ADP iajs-2566 86 11 w w PROPN iajs-2566 86 12 , , PUNCT iajs-2566 86 13 𝔃 𝔃 NOUN iajs-2566 86 14 { { PUNCT iajs-2566 86 15 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 86 16 , , PUNCT iajs-2566 86 17 𝛽 𝛽 NOUN iajs-2566 86 18 , , PUNCT iajs-2566 86 19 𝛼𝑛)}is 𝛼𝑛)}is PROPN iajs-2566 86 20 real real ADJ iajs-2566 86 21 sequence sequence NOUN iajs-2566 86 22 converge converge VERB iajs-2566 86 23 to to ADP iajs-2566 86 24 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 86 25 , , PUNCT iajs-2566 86 26 𝛽 𝛽 NOUN iajs-2566 86 27 , , PUNCT iajs-2566 86 28 𝑀 𝑀 ADP iajs-2566 86 29 ) ) PUNCT iajs-2566 86 30 , , PUNCT iajs-2566 86 31 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 86 32 , , PUNCT iajs-2566 86 33 𝛽 𝛽 PROPN iajs-2566 86 34 , , PUNCT iajs-2566 86 35 𝓏 𝓏 PROPN iajs-2566 86 36 ) ) PUNCT iajs-2566 86 37 since since SCONJ iajs-2566 86 38 the the DET iajs-2566 86 39 converge converge NOUN iajs-2566 86 40 point point NOUN iajs-2566 86 41 is be AUX iajs-2566 86 42 unique unique ADJ iajs-2566 86 43 ∴ ∴ NOUN iajs-2566 86 44 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 86 45 , , PUNCT iajs-2566 86 46 𝛽 𝛽 NOUN iajs-2566 86 47 , , PUNCT iajs-2566 86 48 𝑀 𝑀 ADP iajs-2566 86 49 ) ) PUNCT iajs-2566 86 50 = = SYM iajs-2566 86 51 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 86 52 , , PUNCT iajs-2566 86 53 𝛽 𝛽 NOUN iajs-2566 86 54 , , PUNCT iajs-2566 86 55 𝓏 𝓏 NOUN iajs-2566 86 56 ) ) PUNCT iajs-2566 86 57 βˆ€ βˆ€ PUNCT iajs-2566 87 1 𝛽 𝛽 NOUN iajs-2566 87 2 take take VERB iajs-2566 87 3 𝛽 𝛽 NOUN iajs-2566 87 4 = = SYM iajs-2566 87 5 𝓏 𝓏 PROPN iajs-2566 87 6 then then ADV iajs-2566 87 7 𝐷𝑝(𝓏 𝐷𝑝(𝓏 ADJ iajs-2566 87 8 , , PUNCT iajs-2566 87 9 𝓏 𝓏 X iajs-2566 87 10 , , PUNCT iajs-2566 87 11 𝑀 𝑀 X iajs-2566 87 12 ) ) PUNCT iajs-2566 87 13 = = PUNCT iajs-2566 88 1 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 88 2 , , PUNCT iajs-2566 88 3 𝓏 𝓏 PROPN iajs-2566 88 4 , , PUNCT iajs-2566 88 5 𝓏 𝓏 NOUN iajs-2566 88 6 ) ) PUNCT iajs-2566 88 7 … … PUNCT iajs-2566 88 8 1 1 NUM iajs-2566 88 9 take take VERB iajs-2566 88 10 𝛽 𝛽 NOUN iajs-2566 88 11 = = SYM iajs-2566 88 12 𝑀 𝑀 PROPN iajs-2566 88 13 then then ADV iajs-2566 88 14 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 88 15 , , PUNCT iajs-2566 88 16 𝑀 𝑀 ADP iajs-2566 88 17 , , PUNCT iajs-2566 88 18 𝑀 𝑀 ADP iajs-2566 88 19 ) ) PUNCT iajs-2566 89 1 = = VERB iajs-2566 89 2 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 89 3 , , PUNCT iajs-2566 89 4 𝑀 𝑀 PROPN iajs-2566 89 5 , , PUNCT iajs-2566 89 6 𝓏 𝓏 PROPN iajs-2566 89 7 ) ) PUNCT iajs-2566 89 8 … … PUNCT iajs-2566 89 9 2 2 NUM iajs-2566 89 10 by by ADP iajs-2566 89 11 defying defy VERB iajs-2566 89 12 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 89 13 , , PUNCT iajs-2566 89 14 𝓏 𝓏 PROPN iajs-2566 89 15 , , PUNCT iajs-2566 89 16 𝓏 𝓏 NOUN iajs-2566 89 17 ) ) PUNCT iajs-2566 89 18 ≀ ≀ NUM iajs-2566 89 19 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 89 20 , , PUNCT iajs-2566 89 21 𝛽 𝛽 PROPN iajs-2566 89 22 , , PUNCT iajs-2566 89 23 𝓏 𝓏 PROPN iajs-2566 89 24 ) ) PUNCT iajs-2566 89 25 βˆ€ βˆ€ PUNCT iajs-2566 89 26 𝛽 𝛽 NOUN iajs-2566 89 27 if if SCONJ iajs-2566 89 28 𝛽 𝛽 PROPN iajs-2566 89 29 = = SYM iajs-2566 89 30 𝑀 𝑀 PROPN iajs-2566 89 31 then then ADV iajs-2566 89 32 𝐷𝑝(𝓏 𝐷𝑝(𝓏 VERB iajs-2566 89 33 , , PUNCT iajs-2566 89 34 𝓏 𝓏 PROPN iajs-2566 89 35 , , PUNCT iajs-2566 89 36 𝓏 𝓏 NOUN iajs-2566 89 37 ) ) PUNCT iajs-2566 89 38 ≀ ≀ NOUN iajs-2566 89 39 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 89 40 , , PUNCT iajs-2566 89 41 𝑀 𝑀 PROPN iajs-2566 89 42 , , PUNCT iajs-2566 89 43 𝓏 𝓏 NOUN iajs-2566 89 44 ) ) PUNCT iajs-2566 89 45 = = VERB iajs-2566 89 46 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 89 47 , , PUNCT iajs-2566 89 48 𝑀 𝑀 PART iajs-2566 89 49 , , PUNCT iajs-2566 89 50 𝑀 𝑀 NOUN iajs-2566 89 51 ) ) PUNCT iajs-2566 89 52 ∴ ∴ NOUN iajs-2566 89 53 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 89 54 , , PUNCT iajs-2566 89 55 𝓏 𝓏 PROPN iajs-2566 89 56 , , PUNCT iajs-2566 89 57 𝓏 𝓏 NOUN iajs-2566 89 58 ) ) PUNCT iajs-2566 89 59 ≀ ≀ NOUN iajs-2566 89 60 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 89 61 , , PUNCT iajs-2566 89 62 𝑀 𝑀 X iajs-2566 89 63 , , PUNCT iajs-2566 89 64 𝑀 𝑀 ADP iajs-2566 89 65 ) ) PUNCT iajs-2566 89 66 … … PUNCT iajs-2566 89 67 3 3 NUM iajs-2566 89 68 also also ADV iajs-2566 89 69 , , PUNCT iajs-2566 89 70 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 89 71 , , PUNCT iajs-2566 89 72 𝑀 𝑀 ADP iajs-2566 89 73 , , PUNCT iajs-2566 89 74 𝑀 𝑀 NOUN iajs-2566 89 75 ) ) PUNCT iajs-2566 89 76 ≀ ≀ NUM iajs-2566 89 77 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 89 78 , , PUNCT iajs-2566 89 79 𝛽 𝛽 NOUN iajs-2566 89 80 , , PUNCT iajs-2566 89 81 𝑀 𝑀 NOUN iajs-2566 89 82 ) ) PUNCT iajs-2566 89 83 βˆ€ βˆ€ PUNCT iajs-2566 90 1 𝛽 𝛽 NOUN iajs-2566 90 2 if if SCONJ iajs-2566 90 3 𝛽 𝛽 PROPN iajs-2566 90 4 = = SYM iajs-2566 90 5 𝓏 𝓏 PROPN iajs-2566 90 6 then then ADV iajs-2566 90 7 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 90 8 , , PUNCT iajs-2566 90 9 𝑀 𝑀 PART iajs-2566 90 10 , , PUNCT iajs-2566 90 11 𝑀 𝑀 ADP iajs-2566 90 12 ) ) PUNCT iajs-2566 90 13 ≀ ≀ NOUN iajs-2566 90 14 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 90 15 , , PUNCT iajs-2566 90 16 𝓏 𝓏 X iajs-2566 90 17 , , PUNCT iajs-2566 90 18 𝑀 𝑀 X iajs-2566 90 19 ) ) PUNCT iajs-2566 90 20 = = PUNCT iajs-2566 91 1 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 91 2 , , PUNCT iajs-2566 91 3 𝓏 𝓏 PROPN iajs-2566 91 4 , , PUNCT iajs-2566 91 5 𝓏 𝓏 NOUN iajs-2566 91 6 ) ) PUNCT iajs-2566 91 7 ∴ ∴ NOUN iajs-2566 91 8 𝐷𝑝(𝑀 𝐷𝑝(𝑀 PROPN iajs-2566 91 9 , , PUNCT iajs-2566 91 10 𝑀 𝑀 PART iajs-2566 91 11 , , PUNCT iajs-2566 91 12 𝑀 𝑀 ADP iajs-2566 91 13 ) ) PUNCT iajs-2566 91 14 ≀ ≀ NOUN iajs-2566 91 15 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 91 16 , , PUNCT iajs-2566 91 17 𝓏 𝓏 PROPN iajs-2566 91 18 , , PUNCT iajs-2566 91 19 𝓏 𝓏 NOUN iajs-2566 91 20 ) ) PUNCT iajs-2566 91 21 … … PUNCT iajs-2566 91 22 4 4 NUM iajs-2566 91 23 𝑏𝛽 𝑏𝛽 NOUN iajs-2566 91 24 3 3 NUM iajs-2566 91 25 , , PUNCT iajs-2566 91 26 4 4 NUM iajs-2566 91 27 ; ; PUNCT iajs-2566 91 28 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 91 29 β„Žπ‘Žπ‘£π‘’ β„Žπ‘Žπ‘£π‘’ NOUN iajs-2566 91 30 𝐷𝑝(𝑀 𝐷𝑝(𝑀 PROPN iajs-2566 91 31 , , PUNCT iajs-2566 91 32 𝑀 𝑀 X iajs-2566 91 33 , , PUNCT iajs-2566 91 34 𝑀 𝑀 X iajs-2566 91 35 ) ) PUNCT iajs-2566 91 36 = = PUNCT iajs-2566 92 1 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 92 2 , , PUNCT iajs-2566 92 3 𝓏 𝓏 PROPN iajs-2566 92 4 , , PUNCT iajs-2566 92 5 𝓏 𝓏 NOUN iajs-2566 92 6 ) ) PUNCT iajs-2566 92 7 ∴ ∴ NOUN iajs-2566 92 8 𝐷𝑝(𝑀 𝐷𝑝(𝑀 PROPN iajs-2566 92 9 , , PUNCT iajs-2566 92 10 𝑀 𝑀 PROPN iajs-2566 92 11 , , PUNCT iajs-2566 92 12 𝓏 𝓏 NOUN iajs-2566 92 13 ) ) PUNCT iajs-2566 93 1 = = VERB iajs-2566 93 2 𝐷𝑝(𝑀 𝐷𝑝(𝑀 VERB iajs-2566 93 3 , , PUNCT iajs-2566 93 4 𝑀 𝑀 PART iajs-2566 93 5 , , PUNCT iajs-2566 93 6 𝑀 𝑀 X iajs-2566 93 7 ) ) PUNCT iajs-2566 93 8 = = PUNCT iajs-2566 94 1 𝐷𝑝(𝓏 𝐷𝑝(𝓏 NOUN iajs-2566 94 2 , , PUNCT iajs-2566 94 3 𝓏 𝓏 PROPN iajs-2566 94 4 , , PUNCT iajs-2566 94 5 𝓏 𝓏 NOUN iajs-2566 94 6 ) ) PUNCT iajs-2566 94 7 , , PUNCT iajs-2566 94 8 π‘‘β„Žπ‘’π‘  π‘‘β„Žπ‘’π‘  NOUN iajs-2566 94 9 𝑀 𝑀 NOUN iajs-2566 94 10 = = PUNCT iajs-2566 94 11 𝓏. 𝓏. PROPN iajs-2566 94 12 βŽ• βŽ• PROPN iajs-2566 94 13 example example NOUN iajs-2566 94 14 8 8 NUM iajs-2566 94 15 let let VERB iajs-2566 94 16 π‘Œ π‘Œ PROPN iajs-2566 94 17 = = PUNCT iajs-2566 95 1 [ [ X iajs-2566 95 2 0 0 NUM iajs-2566 95 3 , , PUNCT iajs-2566 95 4 ∞ ∞ PROPN iajs-2566 95 5 ) ) PUNCT iajs-2566 95 6 and and CCONJ iajs-2566 95 7 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 95 8 , , PUNCT iajs-2566 95 9 𝛽 𝛽 PROPN iajs-2566 95 10 , , PUNCT iajs-2566 95 11 𝛾 𝛾 NOUN iajs-2566 95 12 ) ) PUNCT iajs-2566 95 13 = = SYM iajs-2566 95 14 π‘šπ‘Žπ›Ό{𝛼 π‘šπ‘Žπ›Ό{𝛼 NOUN iajs-2566 95 15 , , PUNCT iajs-2566 95 16 𝛽 𝛽 NOUN iajs-2566 95 17 , , PUNCT iajs-2566 95 18 𝛾 𝛾 ADP iajs-2566 95 19 } } PUNCT iajs-2566 95 20 then then ADV iajs-2566 95 21 ( ( PUNCT iajs-2566 95 22 π‘Œ π‘Œ PROPN iajs-2566 95 23 , , PUNCT iajs-2566 95 24 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 95 25 ) ) PUNCT iajs-2566 95 26 is be AUX iajs-2566 95 27 general general ADJ iajs-2566 95 28 partial partial ADJ iajs-2566 95 29 metric metric ADJ iajs-2566 95 30 space space NOUN iajs-2566 95 31 as as SCONJ iajs-2566 95 32 we we PRON iajs-2566 95 33 see see VERB iajs-2566 95 34 in in ADP iajs-2566 95 35 example example NOUN iajs-2566 95 36 2 2 NUM iajs-2566 95 37 , , PUNCT iajs-2566 95 38 if if SCONJ iajs-2566 95 39 𝛼n= 𝛼n= PROPN iajs-2566 95 40 2 2 NUM iajs-2566 95 41 1 1 NUM iajs-2566 95 42 𝑛 𝑛 NOUN iajs-2566 95 43 , , PUNCT iajs-2566 95 44 then then ADV iajs-2566 95 45 the the DET iajs-2566 95 46 sequence sequence NOUN iajs-2566 95 47 { { PUNCT iajs-2566 95 48 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 95 49 } } PUNCT iajs-2566 95 50 is be AUX iajs-2566 95 51 a a DET iajs-2566 95 52 very very ADV iajs-2566 95 53 strongly strongly ADV iajs-2566 95 54 converge converge VERB iajs-2566 95 55 to1 to1 PROPN iajs-2566 95 56 . . PUNCT iajs-2566 96 1 indeed indeed ADV iajs-2566 96 2 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 96 3 , , PUNCT iajs-2566 96 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 96 5 , , PUNCT iajs-2566 96 6 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 96 7 ) ) PUNCT iajs-2566 96 8 = = SYM iajs-2566 96 9 π‘šπ‘Žπ›Ό π‘šπ‘Žπ›Ό NOUN iajs-2566 96 10 { { PUNCT iajs-2566 96 11 2 2 NUM iajs-2566 96 12 1 1 NUM iajs-2566 96 13 𝑛 𝑛 NOUN iajs-2566 96 14 , , PUNCT iajs-2566 96 15 2 2 NUM iajs-2566 96 16 1 1 NUM iajs-2566 96 17 π‘š π‘š NOUN iajs-2566 96 18 , , PUNCT iajs-2566 96 19 1 1 NUM iajs-2566 96 20 } } PUNCT iajs-2566 96 21 β†’ β†’ SYM iajs-2566 96 22 1 1 NUM iajs-2566 96 23 = = SYM iajs-2566 96 24 𝐷𝑝(1 𝐷𝑝(1 NOUN iajs-2566 96 25 , , PUNCT iajs-2566 96 26 1 1 NUM iajs-2566 96 27 , , PUNCT iajs-2566 96 28 1 1 NUM iajs-2566 96 29 ) ) PUNCT iajs-2566 96 30 π‘Žπ‘  π‘Žπ‘  ADP iajs-2566 96 31 𝑛 𝑛 PROPN iajs-2566 96 32 , , PUNCT iajs-2566 96 33 π‘š π‘š PROPN iajs-2566 96 34 β†’ β†’ SYM iajs-2566 96 35 ∞ ∞ NUM iajs-2566 96 36 π΄π‘™π‘ π‘œ π΄π‘™π‘ π‘œ PROPN iajs-2566 96 37 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 96 38 , , PUNCT iajs-2566 96 39 𝛾 𝛾 NOUN iajs-2566 96 40 , , PUNCT iajs-2566 96 41 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 96 42 ) ) PUNCT iajs-2566 96 43 = = PUNCT iajs-2566 97 1 π‘šπ‘Žπ›Ό{𝛽 π‘šπ‘Žπ›Ό{𝛽 PROPN iajs-2566 97 2 , , PUNCT iajs-2566 97 3 𝛾 𝛾 PROPN iajs-2566 97 4 , , PUNCT iajs-2566 97 5 2 2 NUM iajs-2566 97 6 1 1 NUM iajs-2566 97 7 𝑛 𝑛 PROPN iajs-2566 97 8 } } PUNCT iajs-2566 97 9 ⟢ ⟢ NOUN iajs-2566 97 10 π‘šπ‘Žπ›Ό{𝛽 π‘šπ‘Žπ›Ό{𝛽 NOUN iajs-2566 97 11 , , PUNCT iajs-2566 97 12 𝛾 𝛾 NOUN iajs-2566 97 13 , , PUNCT iajs-2566 97 14 1 1 NUM iajs-2566 97 15 } } PUNCT iajs-2566 97 16 π‘Žπ‘  π‘Žπ‘  NOUN iajs-2566 97 17 𝑛 𝑛 PROPN iajs-2566 97 18 β†’ β†’ SYM iajs-2566 97 19 ∞ ∞ NUM iajs-2566 97 20 βˆ€ βˆ€ PUNCT iajs-2566 97 21 𝛽 𝛽 NOUN iajs-2566 97 22 , , PUNCT iajs-2566 97 23 𝛾 𝛾 ADP iajs-2566 97 24 ∈ ∈ NOUN iajs-2566 97 25 π‘Œ π‘Œ PROPN iajs-2566 97 26 remark remark NOUN iajs-2566 97 27 9 9 NUM iajs-2566 97 28 it it PRON iajs-2566 97 29 is be AUX iajs-2566 97 30 clear clear ADJ iajs-2566 97 31 from from ADP iajs-2566 97 32 definition definition NOUN iajs-2566 97 33 that that SCONJ iajs-2566 97 34 every every DET iajs-2566 97 35 very very ADV iajs-2566 97 36 strong strong ADJ iajs-2566 97 37 converge converge NOUN iajs-2566 97 38 sequence sequence NOUN iajs-2566 97 39 is be AUX iajs-2566 97 40 a a DET iajs-2566 97 41 strongly strongly ADV iajs-2566 97 42 converge converge VERB iajs-2566 97 43 , , PUNCT iajs-2566 97 44 so so SCONJ iajs-2566 97 45 that that SCONJ iajs-2566 97 46 if if SCONJ iajs-2566 97 47 { { PUNCT iajs-2566 97 48 𝛼𝑛 𝛼𝑛 X iajs-2566 97 49 } } PUNCT iajs-2566 97 50 is be AUX iajs-2566 97 51 very very ADV iajs-2566 97 52 strongly strongly ADV iajs-2566 97 53 converge converge VERB iajs-2566 97 54 then then ADV iajs-2566 97 55 the the DET iajs-2566 97 56 converge converge NOUN iajs-2566 97 57 point point NOUN iajs-2566 97 58 is be AUX iajs-2566 97 59 unique unique ADJ iajs-2566 97 60 . . PUNCT iajs-2566 98 1 theorem theorem ADJ iajs-2566 98 2 10 10 NUM iajs-2566 98 3 let let NOUN iajs-2566 98 4 ( ( PUNCT iajs-2566 98 5 π‘Œ π‘Œ PROPN iajs-2566 98 6 , , PUNCT iajs-2566 98 7 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 98 8 ) ) PUNCT iajs-2566 98 9 be be AUX iajs-2566 98 10 general general ADJ iajs-2566 98 11 partial partial ADJ iajs-2566 98 12 metric metric ADJ iajs-2566 98 13 space space NOUN iajs-2566 98 14 , , PUNCT iajs-2566 98 15 if if SCONJ iajs-2566 98 16 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PRON iajs-2566 98 17 , , PUNCT iajs-2566 98 18 𝛽 𝛽 NOUN iajs-2566 98 19 , , PUNCT iajs-2566 98 20 𝛾 𝛾 NOUN iajs-2566 98 21 ) ) PUNCT iajs-2566 98 22 = = SYM iajs-2566 99 1 0 0 PUNCT iajs-2566 99 2 then then ADV iajs-2566 99 3 𝛼 𝛼 VERB iajs-2566 99 4 = = SYM iajs-2566 99 5 𝛽 𝛽 NOUN iajs-2566 99 6 = = SYM iajs-2566 99 7 𝛾 𝛾 ADP iajs-2566 99 8 proof proof NOUN iajs-2566 99 9 52 52 NUM iajs-2566 99 10 ibn ibn PROPN iajs-2566 99 11 al al PROPN iajs-2566 99 12 - - PUNCT iajs-2566 99 13 haitham haitham PROPN iajs-2566 99 14 jour jour X iajs-2566 99 15 . . PROPN iajs-2566 100 1 for for ADP iajs-2566 100 2 pure pure ADJ iajs-2566 100 3 & & CCONJ iajs-2566 100 4 appl appl PROPN iajs-2566 100 5 . . PUNCT iajs-2566 101 1 sci sci PROPN iajs-2566 101 2 . . PROPN iajs-2566 102 1 34 34 NUM iajs-2566 102 2 ( ( PUNCT iajs-2566 102 3 1 1 NUM iajs-2566 102 4 ) ) PUNCT iajs-2566 102 5 2021 2021 NUM iajs-2566 102 6 we we PRON iajs-2566 102 7 have have VERB iajs-2566 102 8 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 102 9 , , PUNCT iajs-2566 102 10 𝛼 𝛼 INTJ iajs-2566 102 11 , , PUNCT iajs-2566 102 12 𝛼 𝛼 NOUN iajs-2566 102 13 ) ) PUNCT iajs-2566 102 14 ≀ ≀ PUNCT iajs-2566 103 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 103 2 , , PUNCT iajs-2566 103 3 𝛽 𝛽 PROPN iajs-2566 103 4 , , PUNCT iajs-2566 103 5 𝛾 𝛾 NOUN iajs-2566 103 6 ) ) PUNCT iajs-2566 103 7 = = SYM iajs-2566 103 8 0 0 NUM iajs-2566 103 9 , , PUNCT iajs-2566 103 10 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 103 11 , , PUNCT iajs-2566 103 12 𝛽 𝛽 PROPN iajs-2566 103 13 , , PUNCT iajs-2566 103 14 𝛽 𝛽 NOUN iajs-2566 103 15 ) ) PUNCT iajs-2566 103 16 ≀ ≀ PUNCT iajs-2566 103 17 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 103 18 , , PUNCT iajs-2566 103 19 𝛽 𝛽 PROPN iajs-2566 103 20 , , PUNCT iajs-2566 103 21 𝛾 𝛾 NOUN iajs-2566 103 22 ) ) PUNCT iajs-2566 103 23 = = SYM iajs-2566 103 24 0 0 NUM iajs-2566 103 25 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 103 26 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 103 27 , , PUNCT iajs-2566 103 28 𝛾 𝛾 NOUN iajs-2566 103 29 , , PUNCT iajs-2566 103 30 𝛾 𝛾 NOUN iajs-2566 103 31 ) ) PUNCT iajs-2566 103 32 ≀ ≀ PUNCT iajs-2566 104 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 104 2 ( ( PUNCT iajs-2566 104 3 𝛼 𝛼 INTJ iajs-2566 104 4 , , PUNCT iajs-2566 104 5 𝛽 𝛽 PROPN iajs-2566 104 6 , , PUNCT iajs-2566 104 7 𝛾 𝛾 NOUN iajs-2566 104 8 ) ) PUNCT iajs-2566 104 9 = = SYM iajs-2566 104 10 0 0 NUM iajs-2566 104 11 β‡’ β‡’ PROPN iajs-2566 104 12 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 104 13 ( ( PUNCT iajs-2566 104 14 𝛼 𝛼 INTJ iajs-2566 104 15 , , PUNCT iajs-2566 104 16 𝛼 𝛼 INTJ iajs-2566 104 17 , , PUNCT iajs-2566 104 18 𝛼 𝛼 NOUN iajs-2566 104 19 ) ) PUNCT iajs-2566 104 20 = = SYM iajs-2566 104 21 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 104 22 , , PUNCT iajs-2566 104 23 𝛽 𝛽 NOUN iajs-2566 104 24 , , PUNCT iajs-2566 104 25 𝛽 𝛽 NOUN iajs-2566 104 26 ) ) PUNCT iajs-2566 104 27 = = SYM iajs-2566 105 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 105 2 , , PUNCT iajs-2566 105 3 𝛾 𝛾 NOUN iajs-2566 105 4 , , PUNCT iajs-2566 105 5 𝛾 𝛾 NOUN iajs-2566 105 6 ) ) PUNCT iajs-2566 105 7 = = SYM iajs-2566 106 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 106 2 , , PUNCT iajs-2566 106 3 𝛽 𝛽 NOUN iajs-2566 106 4 , , PUNCT iajs-2566 106 5 𝛾 𝛾 NOUN iajs-2566 106 6 ) ) PUNCT iajs-2566 106 7 = = SYM iajs-2566 106 8 0 0 PUNCT iajs-2566 106 9 therefore therefore ADV iajs-2566 106 10 𝛼 𝛼 PROPN iajs-2566 106 11 = = SYM iajs-2566 106 12 𝛽 𝛽 NOUN iajs-2566 106 13 = = SYM iajs-2566 106 14 𝛾. 𝛾. NOUN iajs-2566 106 15 βŽ• βŽ• PROPN iajs-2566 106 16 remark remark VERB iajs-2566 106 17 11 11 NUM iajs-2566 106 18 if if SCONJ iajs-2566 106 19 𝛼 𝛼 VERB iajs-2566 106 20 = = SYM iajs-2566 106 21 𝛽 𝛽 NOUN iajs-2566 106 22 = = SYM iajs-2566 106 23 𝛾 𝛾 NOUN iajs-2566 106 24 , , PUNCT iajs-2566 106 25 then then ADV iajs-2566 106 26 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 106 27 , , PUNCT iajs-2566 106 28 𝛽 𝛽 NOUN iajs-2566 106 29 , , PUNCT iajs-2566 106 30 𝛾 𝛾 NOUN iajs-2566 106 31 ) ) PUNCT iajs-2566 106 32 may may AUX iajs-2566 106 33 not not PART iajs-2566 106 34 be be AUX iajs-2566 106 35 zero zero NUM iajs-2566 106 36 . . PUNCT iajs-2566 107 1 3 3 X iajs-2566 107 2 . . X iajs-2566 107 3 relations relation NOUN iajs-2566 107 4 between between ADP iajs-2566 107 5 d d NOUN iajs-2566 107 6 - - ADJ iajs-2566 107 7 metric metric ADJ iajs-2566 107 8 , , PUNCT iajs-2566 107 9 partial partial ADJ iajs-2566 107 10 metric metric ADJ iajs-2566 107 11 and and CCONJ iajs-2566 107 12 general general ADJ iajs-2566 107 13 partial partial ADJ iajs-2566 107 14 metric metric ADJ iajs-2566 107 15 spaces space NOUN iajs-2566 107 16 theorem theorem VERB iajs-2566 107 17 12 12 NUM iajs-2566 107 18 let let NOUN iajs-2566 107 19 ( ( PUNCT iajs-2566 107 20 π‘Œ π‘Œ PROPN iajs-2566 107 21 , , PUNCT iajs-2566 107 22 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 107 23 ) ) PUNCT iajs-2566 107 24 be be VERB iajs-2566 107 25 a a DET iajs-2566 107 26 general general ADJ iajs-2566 107 27 partial partial ADJ iajs-2566 107 28 metric metric ADJ iajs-2566 107 29 space space NOUN iajs-2566 107 30 , , PUNCT iajs-2566 107 31 then then ADV iajs-2566 107 32 the the DET iajs-2566 107 33 functions function NOUN iajs-2566 107 34 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 107 35 : : PUNCT iajs-2566 107 36 π‘Œ3 π‘Œ3 PROPN iajs-2566 107 37 β†’ β†’ PUNCT iajs-2566 107 38 [ [ X iajs-2566 107 39 0 0 NUM iajs-2566 107 40 , , PUNCT iajs-2566 107 41 ∞ ∞ NOUN iajs-2566 107 42 ) ) PUNCT iajs-2566 107 43 given give VERB iajs-2566 107 44 by by ADP iajs-2566 107 45 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 107 46 ( ( PUNCT iajs-2566 107 47 𝛼 𝛼 INTJ iajs-2566 107 48 , , PUNCT iajs-2566 107 49 𝛽 𝛽 PROPN iajs-2566 107 50 , , PUNCT iajs-2566 107 51 𝛾 𝛾 NOUN iajs-2566 107 52 ) ) PUNCT iajs-2566 107 53 = = PUNCT iajs-2566 108 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 108 2 , , PUNCT iajs-2566 108 3 𝛼 𝛼 INTJ iajs-2566 108 4 , , PUNCT iajs-2566 108 5 𝛽 𝛽 NOUN iajs-2566 108 6 ) ) PUNCT iajs-2566 109 1 + + CCONJ iajs-2566 109 2 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 109 3 , , PUNCT iajs-2566 109 4 𝛼 𝛼 INTJ iajs-2566 109 5 , , PUNCT iajs-2566 109 6 𝛾 𝛾 NOUN iajs-2566 109 7 ) ) PUNCT iajs-2566 109 8 + + NUM iajs-2566 109 9 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 109 10 , , PUNCT iajs-2566 109 11 𝛽 𝛽 NOUN iajs-2566 109 12 , , PUNCT iajs-2566 109 13 𝛼 𝛼 PROPN iajs-2566 109 14 ) ) PUNCT iajs-2566 109 15 + + NUM iajs-2566 109 16 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 109 17 , , PUNCT iajs-2566 109 18 𝛽 𝛽 NOUN iajs-2566 109 19 , , PUNCT iajs-2566 109 20 𝛾 𝛾 PROPN iajs-2566 109 21 ) ) PUNCT iajs-2566 110 1 + + CCONJ iajs-2566 110 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 110 3 , , PUNCT iajs-2566 110 4 𝛾 𝛾 NOUN iajs-2566 110 5 , , PUNCT iajs-2566 110 6 𝛼 𝛼 NOUN iajs-2566 110 7 ) ) PUNCT iajs-2566 111 1 + + CCONJ iajs-2566 111 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 111 3 , , PUNCT iajs-2566 111 4 𝛾 𝛾 NOUN iajs-2566 111 5 , , PUNCT iajs-2566 111 6 𝛽 𝛽 NOUN iajs-2566 111 7 ) ) PUNCT iajs-2566 111 8 – – PUNCT iajs-2566 112 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 112 2 ( ( PUNCT iajs-2566 112 3 𝛼 𝛼 PROPN iajs-2566 112 4 , , PUNCT iajs-2566 112 5 𝛼 𝛼 INTJ iajs-2566 112 6 , , PUNCT iajs-2566 112 7 𝛼 𝛼 NOUN iajs-2566 112 8 ) ) PUNCT iajs-2566 112 9 – – PUNCT iajs-2566 112 10 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 112 11 ( ( PUNCT iajs-2566 112 12 𝛽 𝛽 NOUN iajs-2566 112 13 , , PUNCT iajs-2566 112 14 𝛽 𝛽 PROPN iajs-2566 112 15 , , PUNCT iajs-2566 112 16 𝛽 𝛽 PROPN iajs-2566 112 17 ) ) PUNCT iajs-2566 112 18 – – PUNCT iajs-2566 112 19 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 112 20 , , PUNCT iajs-2566 112 21 𝛾 𝛾 NOUN iajs-2566 112 22 , , PUNCT iajs-2566 112 23 𝛾 𝛾 NOUN iajs-2566 112 24 ) ) PUNCT iajs-2566 112 25 . . PUNCT iajs-2566 113 1 ( ( PUNCT iajs-2566 113 2 1.1 1.1 NUM iajs-2566 113 3 ) ) PUNCT iajs-2566 113 4 is be AUX iajs-2566 113 5 a a DET iajs-2566 113 6 d d ADJ iajs-2566 113 7 - - ADJ iajs-2566 113 8 metric metric ADJ iajs-2566 113 9 space space NOUN iajs-2566 113 10 on on ADP iajs-2566 113 11 π‘Œ π‘Œ PROPN iajs-2566 113 12 proof proof NOUN iajs-2566 113 13 1 1 NUM iajs-2566 113 14 ) ) PUNCT iajs-2566 113 15 since since SCONJ iajs-2566 113 16 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 113 17 , , PUNCT iajs-2566 113 18 𝛼 𝛼 INTJ iajs-2566 113 19 , , PUNCT iajs-2566 113 20 𝛽 𝛽 NOUN iajs-2566 113 21 ) ) PUNCT iajs-2566 113 22 – – PUNCT iajs-2566 113 23 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 113 24 , , PUNCT iajs-2566 113 25 𝛼 𝛼 INTJ iajs-2566 113 26 , , PUNCT iajs-2566 113 27 𝛼 𝛼 PROPN iajs-2566 113 28 ) ) PUNCT iajs-2566 113 29 β‰₯ β‰₯ NOUN iajs-2566 113 30 0 0 NUM iajs-2566 113 31 , , PUNCT iajs-2566 113 32 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 113 33 , , PUNCT iajs-2566 113 34 𝛼 𝛼 INTJ iajs-2566 113 35 , , PUNCT iajs-2566 113 36 𝛾 𝛾 NOUN iajs-2566 113 37 ) ) PUNCT iajs-2566 113 38 – – PUNCT iajs-2566 113 39 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 113 40 , , PUNCT iajs-2566 113 41 𝛼 𝛼 INTJ iajs-2566 113 42 , , PUNCT iajs-2566 113 43 𝛼 𝛼 NOUN iajs-2566 113 44 ) ) PUNCT iajs-2566 113 45 β‰₯ β‰₯ NOUN iajs-2566 113 46 0 0 NUM iajs-2566 113 47 , , PUNCT iajs-2566 113 48 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 113 49 ( ( PUNCT iajs-2566 113 50 𝛽 𝛽 PROPN iajs-2566 113 51 , , PUNCT iajs-2566 113 52 𝛽 𝛽 PROPN iajs-2566 113 53 , , PUNCT iajs-2566 113 54 𝛼 𝛼 NOUN iajs-2566 113 55 ) ) PUNCT iajs-2566 113 56 – – PUNCT iajs-2566 113 57 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 113 58 ( ( PUNCT iajs-2566 113 59 𝛽 𝛽 PROPN iajs-2566 113 60 , , PUNCT iajs-2566 113 61 𝛽 𝛽 PROPN iajs-2566 113 62 , , PUNCT iajs-2566 113 63 𝛽 𝛽 PROPN iajs-2566 113 64 ) ) PUNCT iajs-2566 113 65 β‰₯ β‰₯ NOUN iajs-2566 113 66 0 0 NUM iajs-2566 113 67 , , PUNCT iajs-2566 113 68 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 113 69 ( ( PUNCT iajs-2566 113 70 𝛽 𝛽 PROPN iajs-2566 113 71 , , PUNCT iajs-2566 113 72 𝛽 𝛽 PROPN iajs-2566 113 73 , , PUNCT iajs-2566 113 74 𝛾 𝛾 NOUN iajs-2566 113 75 ) ) PUNCT iajs-2566 113 76 – – PUNCT iajs-2566 113 77 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 113 78 ( ( PUNCT iajs-2566 113 79 𝛽 𝛽 PROPN iajs-2566 113 80 , , PUNCT iajs-2566 113 81 𝛽 𝛽 PROPN iajs-2566 113 82 , , PUNCT iajs-2566 113 83 𝛽 𝛽 PROPN iajs-2566 113 84 ) ) PUNCT iajs-2566 113 85 β‰₯ β‰₯ NOUN iajs-2566 113 86 0 0 NUM iajs-2566 113 87 , , PUNCT iajs-2566 113 88 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 113 89 , , PUNCT iajs-2566 113 90 𝛾 𝛾 NOUN iajs-2566 113 91 , , PUNCT iajs-2566 113 92 𝛼 𝛼 NOUN iajs-2566 113 93 ) ) PUNCT iajs-2566 113 94 – – PUNCT iajs-2566 113 95 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 113 96 , , PUNCT iajs-2566 113 97 𝛾 𝛾 NOUN iajs-2566 113 98 , , PUNCT iajs-2566 113 99 𝛾 𝛾 NOUN iajs-2566 113 100 ) ) PUNCT iajs-2566 113 101 β‰₯ β‰₯ NOUN iajs-2566 113 102 0 0 NUM iajs-2566 113 103 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 113 104 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 113 105 , , PUNCT iajs-2566 113 106 𝛾 𝛾 NOUN iajs-2566 113 107 , , PUNCT iajs-2566 113 108 𝛽 𝛽 NOUN iajs-2566 113 109 ) ) PUNCT iajs-2566 113 110 – – PUNCT iajs-2566 113 111 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 113 112 , , PUNCT iajs-2566 113 113 𝛾 𝛾 NOUN iajs-2566 113 114 , , PUNCT iajs-2566 113 115 𝛾 𝛾 NOUN iajs-2566 113 116 ) ) PUNCT iajs-2566 113 117 β‰₯ β‰₯ NOUN iajs-2566 113 118 0 0 NUM iajs-2566 113 119 π‘ π‘œ π‘ π‘œ ADP iajs-2566 113 120 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 113 121 ( ( PUNCT iajs-2566 113 122 𝛼 𝛼 INTJ iajs-2566 113 123 , , PUNCT iajs-2566 113 124 𝛽 𝛽 PROPN iajs-2566 113 125 , , PUNCT iajs-2566 113 126 𝛾 𝛾 PROPN iajs-2566 113 127 ) ) PUNCT iajs-2566 113 128 β‰₯ β‰₯ NOUN iajs-2566 113 129 0 0 NUM iajs-2566 113 130 . . NOUN iajs-2566 113 131 2 2 X iajs-2566 113 132 ) ) PUNCT iajs-2566 113 133 𝐼𝑓 𝐼𝑓 PROPN iajs-2566 113 134 𝐷𝑔(𝛼 𝐷𝑔(𝛼 PROPN iajs-2566 113 135 , , PUNCT iajs-2566 113 136 𝛽 𝛽 PROPN iajs-2566 113 137 , , PUNCT iajs-2566 113 138 𝛾 𝛾 NOUN iajs-2566 113 139 ) ) PUNCT iajs-2566 113 140 = = SYM iajs-2566 113 141 0 0 NUM iajs-2566 113 142 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› NOUN iajs-2566 113 143 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 113 144 ( ( PUNCT iajs-2566 113 145 𝛼 𝛼 INTJ iajs-2566 113 146 , , PUNCT iajs-2566 113 147 𝛼 𝛼 INTJ iajs-2566 113 148 , , PUNCT iajs-2566 113 149 𝛽 𝛽 NOUN iajs-2566 113 150 ) ) PUNCT iajs-2566 114 1 + + PUNCT iajs-2566 115 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 115 2 ( ( PUNCT iajs-2566 115 3 𝛼 𝛼 INTJ iajs-2566 115 4 , , PUNCT iajs-2566 115 5 𝛼 𝛼 INTJ iajs-2566 115 6 , , PUNCT iajs-2566 115 7 𝛾 𝛾 NOUN iajs-2566 115 8 ) ) PUNCT iajs-2566 115 9 + + PUNCT iajs-2566 116 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 116 2 ( ( PUNCT iajs-2566 116 3 𝛽 𝛽 PROPN iajs-2566 116 4 , , PUNCT iajs-2566 116 5 𝛽 𝛽 PROPN iajs-2566 116 6 , , PUNCT iajs-2566 116 7 𝛼 𝛼 PROPN iajs-2566 116 8 ) ) PUNCT iajs-2566 116 9 + + PUNCT iajs-2566 117 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 117 2 ( ( PUNCT iajs-2566 117 3 𝛽 𝛽 PROPN iajs-2566 117 4 , , PUNCT iajs-2566 117 5 𝛽 𝛽 PROPN iajs-2566 117 6 , , PUNCT iajs-2566 117 7 𝛾 𝛾 PROPN iajs-2566 117 8 ) ) PUNCT iajs-2566 118 1 + + CCONJ iajs-2566 118 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 118 3 , , PUNCT iajs-2566 118 4 𝛾 𝛾 NOUN iajs-2566 118 5 , , PUNCT iajs-2566 118 6 𝛼 𝛼 X iajs-2566 118 7 ) ) PUNCT iajs-2566 119 1 + + CCONJ iajs-2566 119 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 119 3 , , PUNCT iajs-2566 119 4 𝛾 𝛾 NOUN iajs-2566 119 5 𝛽 𝛽 NOUN iajs-2566 119 6 ) ) PUNCT iajs-2566 119 7 – – PUNCT iajs-2566 120 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 120 2 ( ( PUNCT iajs-2566 120 3 𝛼 𝛼 PROPN iajs-2566 120 4 , , PUNCT iajs-2566 120 5 𝛼 𝛼 INTJ iajs-2566 120 6 , , PUNCT iajs-2566 120 7 𝛼 𝛼 NOUN iajs-2566 120 8 ) ) PUNCT iajs-2566 120 9 – – PUNCT iajs-2566 120 10 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 120 11 ( ( PUNCT iajs-2566 120 12 𝛽 𝛽 NOUN iajs-2566 120 13 , , PUNCT iajs-2566 120 14 𝛽 𝛽 PROPN iajs-2566 120 15 , , PUNCT iajs-2566 120 16 𝛽 𝛽 PROPN iajs-2566 120 17 ) ) PUNCT iajs-2566 120 18 – – PUNCT iajs-2566 120 19 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 120 20 , , PUNCT iajs-2566 120 21 𝛾 𝛾 NOUN iajs-2566 120 22 𝛾 𝛾 NOUN iajs-2566 120 23 ) ) PUNCT iajs-2566 120 24 = = SYM iajs-2566 120 25 0 0 NUM iajs-2566 121 1 π‘‡π‘Žπ‘˜π‘’ π‘‡π‘Žπ‘˜π‘’ PROPN iajs-2566 121 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 121 3 ( ( PUNCT iajs-2566 121 4 𝛼 𝛼 PROPN iajs-2566 121 5 , , PUNCT iajs-2566 121 6 𝛼 𝛼 X iajs-2566 121 7 , , PUNCT iajs-2566 121 8 𝛽 𝛽 NOUN iajs-2566 121 9 ) ) PUNCT iajs-2566 121 10 + + PUNCT iajs-2566 122 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 122 2 ( ( PUNCT iajs-2566 122 3 𝛼 𝛼 PROPN iajs-2566 122 4 , , PUNCT iajs-2566 122 5 𝛼 𝛼 X iajs-2566 122 6 , , PUNCT iajs-2566 122 7 𝛾 𝛾 NOUN iajs-2566 122 8 ) ) PUNCT iajs-2566 122 9 βˆ’ βˆ’ NOUN iajs-2566 123 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 123 2 ( ( PUNCT iajs-2566 123 3 𝛼 𝛼 PROPN iajs-2566 123 4 , , PUNCT iajs-2566 123 5 𝛼 𝛼 X iajs-2566 123 6 , , PUNCT iajs-2566 123 7 𝛼 𝛼 NOUN iajs-2566 123 8 ) ) PUNCT iajs-2566 123 9 = = SYM iajs-2566 123 10 0 0 NUM iajs-2566 123 11 β‡’ β‡’ NOUN iajs-2566 123 12 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 123 13 ( ( PUNCT iajs-2566 123 14 𝛼 𝛼 PROPN iajs-2566 123 15 , , PUNCT iajs-2566 123 16 𝛼 𝛼 X iajs-2566 123 17 , , PUNCT iajs-2566 123 18 𝛼 𝛼 NOUN iajs-2566 123 19 ) ) PUNCT iajs-2566 123 20 = = SYM iajs-2566 124 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 124 2 ( ( PUNCT iajs-2566 124 3 𝛼 𝛼 PROPN iajs-2566 124 4 , , PUNCT iajs-2566 124 5 𝛼 𝛼 X iajs-2566 124 6 , , PUNCT iajs-2566 124 7 𝛽 𝛽 NOUN iajs-2566 124 8 ) ) PUNCT iajs-2566 124 9 + + PUNCT iajs-2566 125 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 125 2 ( ( PUNCT iajs-2566 125 3 𝛼 𝛼 PROPN iajs-2566 125 4 , , PUNCT iajs-2566 125 5 𝛼 𝛼 X iajs-2566 125 6 , , PUNCT iajs-2566 125 7 𝛾 𝛾 NOUN iajs-2566 125 8 ) ) PUNCT iajs-2566 125 9 … … PUNCT iajs-2566 125 10 1 1 NUM iajs-2566 125 11 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 125 12 ( ( PUNCT iajs-2566 125 13 𝛼 𝛼 PROPN iajs-2566 125 14 , , PUNCT iajs-2566 125 15 𝛼 𝛼 X iajs-2566 125 16 , , PUNCT iajs-2566 125 17 𝛾 𝛾 NOUN iajs-2566 125 18 ) ) PUNCT iajs-2566 125 19 + + CCONJ iajs-2566 126 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 126 2 ( ( PUNCT iajs-2566 126 3 𝛽 𝛽 PROPN iajs-2566 126 4 , , PUNCT iajs-2566 126 5 𝛽 𝛽 PROPN iajs-2566 126 6 , , PUNCT iajs-2566 126 7 𝛼 𝛼 NOUN iajs-2566 126 8 ) ) PUNCT iajs-2566 126 9 βˆ’ βˆ’ ADP iajs-2566 127 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 127 2 ( ( PUNCT iajs-2566 127 3 𝛼 𝛼 PROPN iajs-2566 127 4 , , PUNCT iajs-2566 127 5 𝛼 𝛼 X iajs-2566 127 6 , , PUNCT iajs-2566 127 7 𝛼 𝛼 NOUN iajs-2566 127 8 ) ) PUNCT iajs-2566 127 9 = = SYM iajs-2566 127 10 0 0 NUM iajs-2566 127 11 β‡’ β‡’ NOUN iajs-2566 127 12 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 127 13 ( ( PUNCT iajs-2566 127 14 𝛼 𝛼 PROPN iajs-2566 127 15 , , PUNCT iajs-2566 127 16 𝛼 𝛼 X iajs-2566 127 17 , , PUNCT iajs-2566 127 18 𝛼 𝛼 NOUN iajs-2566 127 19 ) ) PUNCT iajs-2566 127 20 = = SYM iajs-2566 128 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 128 2 ( ( PUNCT iajs-2566 128 3 𝛼 𝛼 PROPN iajs-2566 128 4 , , PUNCT iajs-2566 128 5 𝛼 𝛼 X iajs-2566 128 6 , , PUNCT iajs-2566 128 7 𝛾 𝛾 NOUN iajs-2566 128 8 ) ) PUNCT iajs-2566 128 9 + + CCONJ iajs-2566 129 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 129 2 ( ( PUNCT iajs-2566 129 3 𝛽 𝛽 PROPN iajs-2566 129 4 , , PUNCT iajs-2566 129 5 𝛽 𝛽 PROPN iajs-2566 129 6 , , PUNCT iajs-2566 129 7 𝛼 𝛼 NOUN iajs-2566 129 8 ) ) PUNCT iajs-2566 129 9 … … PUNCT iajs-2566 129 10 2 2 NUM iajs-2566 129 11 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 129 12 1&2 1&2 NUM iajs-2566 129 13 , , PUNCT iajs-2566 129 14 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 129 15 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 129 16 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 129 17 ( ( PUNCT iajs-2566 129 18 𝛼 𝛼 PROPN iajs-2566 129 19 , , PUNCT iajs-2566 129 20 𝛼 𝛼 X iajs-2566 129 21 , , PUNCT iajs-2566 129 22 𝛽 𝛽 NOUN iajs-2566 129 23 ) ) PUNCT iajs-2566 129 24 + + PUNCT iajs-2566 130 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 130 2 ( ( PUNCT iajs-2566 130 3 𝛼 𝛼 PROPN iajs-2566 130 4 , , PUNCT iajs-2566 130 5 𝛼 𝛼 X iajs-2566 130 6 , , PUNCT iajs-2566 130 7 𝛾 𝛾 NOUN iajs-2566 130 8 ) ) PUNCT iajs-2566 130 9 = = SYM iajs-2566 131 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 131 2 ( ( PUNCT iajs-2566 131 3 𝛼 𝛼 PROPN iajs-2566 131 4 , , PUNCT iajs-2566 131 5 𝛼 𝛼 X iajs-2566 131 6 , , PUNCT iajs-2566 131 7 𝛾 𝛾 NOUN iajs-2566 131 8 ) ) PUNCT iajs-2566 131 9 + + CCONJ iajs-2566 132 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 132 2 ( ( PUNCT iajs-2566 132 3 𝛽 𝛽 PROPN iajs-2566 132 4 , , PUNCT iajs-2566 132 5 𝛽 𝛽 PROPN iajs-2566 132 6 , , PUNCT iajs-2566 132 7 𝛼 𝛼 NOUN iajs-2566 132 8 ) ) PUNCT iajs-2566 132 9 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› VERB iajs-2566 132 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 132 11 ( ( PUNCT iajs-2566 132 12 𝛼 𝛼 PROPN iajs-2566 132 13 , , PUNCT iajs-2566 132 14 𝛼 𝛼 X iajs-2566 132 15 , , PUNCT iajs-2566 132 16 𝛽 𝛽 NOUN iajs-2566 132 17 ) ) PUNCT iajs-2566 132 18 = = SYM iajs-2566 133 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 133 2 ( ( PUNCT iajs-2566 133 3 𝛽 𝛽 PROPN iajs-2566 133 4 , , PUNCT iajs-2566 133 5 𝛽 𝛽 PROPN iajs-2566 133 6 , , PUNCT iajs-2566 133 7 𝛼 𝛼 NOUN iajs-2566 133 8 ) ) PUNCT iajs-2566 133 9 … … PUNCT iajs-2566 133 10 3 3 NUM iajs-2566 133 11 𝑆𝑖𝑛𝑐𝑒 𝑆𝑖𝑛𝑐𝑒 PROPN iajs-2566 133 12 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 133 13 ( ( PUNCT iajs-2566 133 14 𝛼 𝛼 PROPN iajs-2566 133 15 , , PUNCT iajs-2566 133 16 𝛼 𝛼 X iajs-2566 133 17 , , PUNCT iajs-2566 133 18 𝛼 𝛼 NOUN iajs-2566 133 19 ) ) PUNCT iajs-2566 133 20 = = SYM iajs-2566 134 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 134 2 ( ( PUNCT iajs-2566 134 3 𝛼 𝛼 PROPN iajs-2566 134 4 , , PUNCT iajs-2566 134 5 𝛼 𝛼 X iajs-2566 134 6 , , PUNCT iajs-2566 134 7 𝛽 𝛽 NOUN iajs-2566 134 8 ) ) PUNCT iajs-2566 134 9 + + PUNCT iajs-2566 135 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 135 2 ( ( PUNCT iajs-2566 135 3 𝛼 𝛼 PROPN iajs-2566 135 4 , , PUNCT iajs-2566 135 5 𝛽 𝛽 NOUN iajs-2566 135 6 , , PUNCT iajs-2566 135 7 𝛽 𝛽 NOUN iajs-2566 135 8 ) ) PUNCT iajs-2566 135 9 = = SYM iajs-2566 136 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 136 2 ( ( PUNCT iajs-2566 136 3 𝛼 𝛼 PROPN iajs-2566 136 4 , , PUNCT iajs-2566 136 5 𝛼 𝛼 X iajs-2566 136 6 , , PUNCT iajs-2566 136 7 𝛽 𝛽 NOUN iajs-2566 136 8 ) ) PUNCT iajs-2566 136 9 + + PUNCT iajs-2566 137 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 137 2 ( ( PUNCT iajs-2566 137 3 𝛼 𝛼 PROPN iajs-2566 137 4 , , PUNCT iajs-2566 137 5 𝛼 𝛼 X iajs-2566 137 6 , , PUNCT iajs-2566 137 7 𝛽 𝛽 NOUN iajs-2566 137 8 ) ) PUNCT iajs-2566 137 9 = = PUNCT iajs-2566 138 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 138 2 ( ( PUNCT iajs-2566 138 3 𝛼 𝛼 PROPN iajs-2566 138 4 , , PUNCT iajs-2566 138 5 𝛼 𝛼 X iajs-2566 138 6 , , PUNCT iajs-2566 138 7 𝛽 𝛽 NOUN iajs-2566 138 8 ) ) PUNCT iajs-2566 138 9 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 138 10 , , PUNCT iajs-2566 138 11 𝛼 𝛼 X iajs-2566 138 12 , , PUNCT iajs-2566 138 13 𝛼 𝛼 NOUN iajs-2566 138 14 ) ) PUNCT iajs-2566 138 15 = = SYM iajs-2566 139 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 139 2 ( ( PUNCT iajs-2566 139 3 𝛼 𝛼 PROPN iajs-2566 139 4 , , PUNCT iajs-2566 139 5 𝛼 𝛼 X iajs-2566 139 6 , , PUNCT iajs-2566 139 7 𝛽 𝛽 NOUN iajs-2566 139 8 ) ) PUNCT iajs-2566 139 9 … … PUNCT iajs-2566 139 10 4 4 NUM iajs-2566 139 11 π‘π‘œπ‘€ π‘π‘œπ‘€ PROPN iajs-2566 139 12 , , PUNCT iajs-2566 139 13 π‘‘π‘Žπ‘˜π‘’ π‘‘π‘Žπ‘˜π‘’ PROPN iajs-2566 139 14 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 139 15 ( ( PUNCT iajs-2566 139 16 𝛽 𝛽 PROPN iajs-2566 139 17 , , PUNCT iajs-2566 139 18 𝛽 𝛽 NOUN iajs-2566 139 19 , , PUNCT iajs-2566 139 20 𝛾 𝛾 NOUN iajs-2566 139 21 ) ) PUNCT iajs-2566 139 22 + + CCONJ iajs-2566 140 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 140 2 ( ( PUNCT iajs-2566 140 3 𝛽 𝛽 PROPN iajs-2566 140 4 , , PUNCT iajs-2566 140 5 𝛽 𝛽 PROPN iajs-2566 140 6 , , PUNCT iajs-2566 140 7 𝛼 𝛼 NOUN iajs-2566 140 8 ) ) PUNCT iajs-2566 140 9 βˆ’ βˆ’ ADP iajs-2566 141 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 141 2 ( ( PUNCT iajs-2566 141 3 𝛽 𝛽 PROPN iajs-2566 141 4 , , PUNCT iajs-2566 141 5 𝛽 𝛽 PROPN iajs-2566 141 6 , , PUNCT iajs-2566 141 7 𝛽 𝛽 NOUN iajs-2566 141 8 ) ) PUNCT iajs-2566 141 9 = = SYM iajs-2566 141 10 0 0 NUM iajs-2566 142 1 53 53 NUM iajs-2566 142 2 ibn ibn PROPN iajs-2566 142 3 al al PROPN iajs-2566 142 4 - - PUNCT iajs-2566 142 5 haitham haitham PROPN iajs-2566 142 6 jour jour X iajs-2566 142 7 . . PROPN iajs-2566 142 8 for for ADP iajs-2566 142 9 pure pure ADJ iajs-2566 142 10 & & CCONJ iajs-2566 142 11 appl appl PROPN iajs-2566 142 12 . . PUNCT iajs-2566 143 1 sci sci PROPN iajs-2566 143 2 . . PROPN iajs-2566 144 1 34 34 NUM iajs-2566 144 2 ( ( PUNCT iajs-2566 144 3 1 1 NUM iajs-2566 144 4 ) ) PUNCT iajs-2566 144 5 2021 2021 NUM iajs-2566 144 6 β‡’ β‡’ NOUN iajs-2566 144 7 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 144 8 ( ( PUNCT iajs-2566 144 9 𝛽 𝛽 NOUN iajs-2566 144 10 , , PUNCT iajs-2566 144 11 𝛽 𝛽 PROPN iajs-2566 144 12 , , PUNCT iajs-2566 144 13 𝛽 𝛽 NOUN iajs-2566 144 14 ) ) PUNCT iajs-2566 144 15 = = SYM iajs-2566 145 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 145 2 ( ( PUNCT iajs-2566 145 3 𝛽 𝛽 PROPN iajs-2566 145 4 , , PUNCT iajs-2566 145 5 𝛽 𝛽 NOUN iajs-2566 145 6 , , PUNCT iajs-2566 145 7 𝛾 𝛾 NOUN iajs-2566 145 8 ) ) PUNCT iajs-2566 145 9 + + CCONJ iajs-2566 146 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 146 2 ( ( PUNCT iajs-2566 146 3 𝛽 𝛽 PROPN iajs-2566 146 4 , , PUNCT iajs-2566 146 5 𝛽 𝛽 PROPN iajs-2566 146 6 , , PUNCT iajs-2566 146 7 𝛼 𝛼 NOUN iajs-2566 146 8 ) ) PUNCT iajs-2566 146 9 … … PUNCT iajs-2566 146 10 5 5 NUM iajs-2566 146 11 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 146 12 ( ( PUNCT iajs-2566 146 13 𝛼 𝛼 PROPN iajs-2566 146 14 , , PUNCT iajs-2566 146 15 𝛼 𝛼 X iajs-2566 146 16 , , PUNCT iajs-2566 146 17 𝛽 𝛽 NOUN iajs-2566 146 18 ) ) PUNCT iajs-2566 146 19 + + PUNCT iajs-2566 147 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 147 2 ( ( PUNCT iajs-2566 147 3 𝛽 𝛽 PROPN iajs-2566 147 4 , , PUNCT iajs-2566 147 5 𝛽 𝛽 NOUN iajs-2566 147 6 , , PUNCT iajs-2566 147 7 𝛾 𝛾 NOUN iajs-2566 147 8 ) ) PUNCT iajs-2566 147 9 βˆ’ βˆ’ ADP iajs-2566 148 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 148 2 ( ( PUNCT iajs-2566 148 3 𝛽 𝛽 PROPN iajs-2566 148 4 , , PUNCT iajs-2566 148 5 𝛽 𝛽 PROPN iajs-2566 148 6 , , PUNCT iajs-2566 148 7 𝛽 𝛽 NOUN iajs-2566 148 8 ) ) PUNCT iajs-2566 148 9 = = SYM iajs-2566 148 10 0 0 NUM iajs-2566 148 11 β‡’ β‡’ NOUN iajs-2566 148 12 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 148 13 ( ( PUNCT iajs-2566 148 14 𝛽 𝛽 NOUN iajs-2566 148 15 , , PUNCT iajs-2566 148 16 𝛽 𝛽 PROPN iajs-2566 148 17 , , PUNCT iajs-2566 148 18 𝛽 𝛽 NOUN iajs-2566 148 19 ) ) PUNCT iajs-2566 148 20 = = SYM iajs-2566 149 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 149 2 ( ( PUNCT iajs-2566 149 3 𝛼 𝛼 PROPN iajs-2566 149 4 , , PUNCT iajs-2566 149 5 𝛼 𝛼 X iajs-2566 149 6 , , PUNCT iajs-2566 149 7 𝛽 𝛽 NOUN iajs-2566 149 8 ) ) PUNCT iajs-2566 149 9 + + PUNCT iajs-2566 150 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 150 2 ( ( PUNCT iajs-2566 150 3 𝛽 𝛽 PROPN iajs-2566 150 4 , , PUNCT iajs-2566 150 5 𝛽 𝛽 NOUN iajs-2566 150 6 , , PUNCT iajs-2566 150 7 𝛾 𝛾 PROPN iajs-2566 150 8 ) ) PUNCT iajs-2566 150 9 … … PUNCT iajs-2566 150 10 6 6 NUM iajs-2566 150 11 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 150 12 5&6 5&6 NOUN iajs-2566 150 13 , , PUNCT iajs-2566 150 14 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 150 15 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 150 16 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 150 17 ( ( PUNCT iajs-2566 150 18 𝛽 𝛽 PROPN iajs-2566 150 19 , , PUNCT iajs-2566 150 20 𝛽 𝛽 PROPN iajs-2566 150 21 , , PUNCT iajs-2566 150 22 𝛼 𝛼 NOUN iajs-2566 150 23 ) ) PUNCT iajs-2566 150 24 + + PUNCT iajs-2566 151 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 151 2 ( ( PUNCT iajs-2566 151 3 𝛽 𝛽 PROPN iajs-2566 151 4 , , PUNCT iajs-2566 151 5 𝛽 𝛽 NOUN iajs-2566 151 6 , , PUNCT iajs-2566 151 7 𝛾 𝛾 NOUN iajs-2566 151 8 ) ) PUNCT iajs-2566 151 9 = = SYM iajs-2566 152 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 152 2 ( ( PUNCT iajs-2566 152 3 𝛼 𝛼 PROPN iajs-2566 152 4 , , PUNCT iajs-2566 152 5 𝛼 𝛼 X iajs-2566 152 6 , , PUNCT iajs-2566 152 7 𝛽 𝛽 NOUN iajs-2566 152 8 ) ) PUNCT iajs-2566 152 9 + + PUNCT iajs-2566 153 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 153 2 ( ( PUNCT iajs-2566 153 3 𝛽 𝛽 PROPN iajs-2566 153 4 , , PUNCT iajs-2566 153 5 𝛽 𝛽 NOUN iajs-2566 153 6 , , PUNCT iajs-2566 153 7 𝛾 𝛾 NOUN iajs-2566 153 8 ) ) PUNCT iajs-2566 153 9 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› VERB iajs-2566 153 10 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 153 11 , , PUNCT iajs-2566 153 12 𝛽 𝛽 NOUN iajs-2566 153 13 , , PUNCT iajs-2566 153 14 𝛼 𝛼 NOUN iajs-2566 153 15 ) ) PUNCT iajs-2566 153 16 = = SYM iajs-2566 154 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 154 2 ( ( PUNCT iajs-2566 154 3 𝛼 𝛼 PROPN iajs-2566 154 4 , , PUNCT iajs-2566 154 5 𝛼 𝛼 X iajs-2566 154 6 , , PUNCT iajs-2566 154 7 𝛽 𝛽 NOUN iajs-2566 154 8 ) ) PUNCT iajs-2566 154 9 … … PUNCT iajs-2566 154 10 7 7 NUM iajs-2566 154 11 𝑆𝑖𝑛𝑐𝑒 𝑆𝑖𝑛𝑐𝑒 PROPN iajs-2566 154 12 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 154 13 ( ( PUNCT iajs-2566 154 14 𝛽 𝛽 NOUN iajs-2566 154 15 , , PUNCT iajs-2566 154 16 𝛽 𝛽 PROPN iajs-2566 154 17 , , PUNCT iajs-2566 154 18 𝛽 𝛽 NOUN iajs-2566 154 19 ) ) PUNCT iajs-2566 154 20 = = SYM iajs-2566 155 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 155 2 ( ( PUNCT iajs-2566 155 3 𝛽 𝛽 PROPN iajs-2566 155 4 , , PUNCT iajs-2566 155 5 𝛽 𝛽 PROPN iajs-2566 155 6 , , PUNCT iajs-2566 155 7 𝛼 𝛼 NOUN iajs-2566 155 8 ) ) PUNCT iajs-2566 155 9 + + PUNCT iajs-2566 156 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 156 2 ( ( PUNCT iajs-2566 156 3 𝛼 𝛼 PROPN iajs-2566 156 4 , , PUNCT iajs-2566 156 5 𝛼 𝛼 X iajs-2566 156 6 , , PUNCT iajs-2566 156 7 𝛽 𝛽 NOUN iajs-2566 156 8 ) ) PUNCT iajs-2566 156 9 = = SYM iajs-2566 157 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 157 2 ( ( PUNCT iajs-2566 157 3 𝛼 𝛼 PROPN iajs-2566 157 4 , , PUNCT iajs-2566 157 5 𝛼 𝛼 X iajs-2566 157 6 , , PUNCT iajs-2566 157 7 𝛽 𝛽 NOUN iajs-2566 157 8 ) ) PUNCT iajs-2566 157 9 + + PUNCT iajs-2566 158 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 158 2 ( ( PUNCT iajs-2566 158 3 𝛼 𝛼 PROPN iajs-2566 158 4 , , PUNCT iajs-2566 158 5 𝛼 𝛼 X iajs-2566 158 6 , , PUNCT iajs-2566 158 7 𝛽 𝛽 NOUN iajs-2566 158 8 ) ) PUNCT iajs-2566 158 9 = = SYM iajs-2566 159 1 2𝐷𝑝(𝛼 2𝐷𝑝(𝛼 NUM iajs-2566 159 2 , , PUNCT iajs-2566 159 3 𝛼 𝛼 PROPN iajs-2566 159 4 , , PUNCT iajs-2566 159 5 𝛽 𝛽 NOUN iajs-2566 159 6 ) ) PUNCT iajs-2566 159 7 β‡’ β‡’ VERB iajs-2566 159 8 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 159 9 ( ( PUNCT iajs-2566 159 10 𝛽 𝛽 PROPN iajs-2566 159 11 , , PUNCT iajs-2566 159 12 𝛽 𝛽 PROPN iajs-2566 159 13 , , PUNCT iajs-2566 159 14 𝛽 𝛽 NOUN iajs-2566 159 15 ) ) PUNCT iajs-2566 159 16 = = SYM iajs-2566 160 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 160 2 ( ( PUNCT iajs-2566 160 3 𝛼 𝛼 PROPN iajs-2566 160 4 , , PUNCT iajs-2566 160 5 𝛼 𝛼 X iajs-2566 160 6 , , PUNCT iajs-2566 160 7 𝛽 𝛽 NOUN iajs-2566 160 8 ) ) PUNCT iajs-2566 160 9 … … PUNCT iajs-2566 160 10 8 8 NUM iajs-2566 160 11 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 160 12 4&8 4&8 NOUN iajs-2566 160 13 , , PUNCT iajs-2566 160 14 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 160 15 𝑔𝑒𝑑𝐷𝑝 𝑔𝑒𝑑𝐷𝑝 PROPN iajs-2566 160 16 ( ( PUNCT iajs-2566 160 17 𝛼 𝛼 PROPN iajs-2566 160 18 , , PUNCT iajs-2566 160 19 𝛼 𝛼 X iajs-2566 160 20 , , PUNCT iajs-2566 160 21 𝛼 𝛼 NOUN iajs-2566 160 22 ) ) PUNCT iajs-2566 160 23 = = SYM iajs-2566 161 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 161 2 ( ( PUNCT iajs-2566 161 3 𝛼 𝛼 PROPN iajs-2566 161 4 , , PUNCT iajs-2566 161 5 𝛼 𝛼 X iajs-2566 161 6 , , PUNCT iajs-2566 161 7 𝛽 𝛽 NOUN iajs-2566 161 8 ) ) PUNCT iajs-2566 161 9 = = SYM iajs-2566 162 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 162 2 ( ( PUNCT iajs-2566 162 3 𝛽 𝛽 PROPN iajs-2566 162 4 , , PUNCT iajs-2566 162 5 𝛽 𝛽 PROPN iajs-2566 162 6 , , PUNCT iajs-2566 162 7 𝛽 𝛽 NOUN iajs-2566 162 8 ) ) PUNCT iajs-2566 162 9 π‘ π‘œ π‘ π‘œ ADP iajs-2566 162 10 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 162 11 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› NOUN iajs-2566 162 12 𝛼 𝛼 PROPN iajs-2566 162 13 = = PROPN iajs-2566 162 14 𝛽 𝛽 PROPN iajs-2566 162 15 … … PUNCT iajs-2566 162 16 9 9 NUM iajs-2566 162 17 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 162 18 π‘‘π‘Žπ‘˜π‘’ π‘‘π‘Žπ‘˜π‘’ NOUN iajs-2566 162 19 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 162 20 , , PUNCT iajs-2566 162 21 𝛾 𝛾 NOUN iajs-2566 162 22 , , PUNCT iajs-2566 162 23 𝛼 𝛼 NOUN iajs-2566 162 24 ) ) PUNCT iajs-2566 162 25 + + CCONJ iajs-2566 162 26 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 162 27 , , PUNCT iajs-2566 162 28 𝛾 𝛾 NOUN iajs-2566 162 29 , , PUNCT iajs-2566 162 30 𝛽 𝛽 NOUN iajs-2566 162 31 ) ) PUNCT iajs-2566 162 32 βˆ’ βˆ’ PROPN iajs-2566 163 1 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 163 2 , , PUNCT iajs-2566 163 3 𝛾 𝛾 NOUN iajs-2566 163 4 , , PUNCT iajs-2566 163 5 𝛾 𝛾 NOUN iajs-2566 163 6 ) ) PUNCT iajs-2566 163 7 = = SYM iajs-2566 163 8 0 0 NUM iajs-2566 163 9 β‡’ β‡’ PROPN iajs-2566 163 10 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 163 11 , , PUNCT iajs-2566 163 12 𝛾 𝛾 NOUN iajs-2566 163 13 , , PUNCT iajs-2566 163 14 𝛾 𝛾 NOUN iajs-2566 163 15 ) ) PUNCT iajs-2566 163 16 = = SYM iajs-2566 164 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 164 2 , , PUNCT iajs-2566 164 3 𝛾 𝛾 NOUN iajs-2566 164 4 , , PUNCT iajs-2566 164 5 𝛼 𝛼 NOUN iajs-2566 164 6 ) ) PUNCT iajs-2566 164 7 + + CCONJ iajs-2566 164 8 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 164 9 , , PUNCT iajs-2566 164 10 𝛾 𝛾 NOUN iajs-2566 164 11 , , PUNCT iajs-2566 164 12 𝛽 𝛽 NOUN iajs-2566 164 13 ) ) PUNCT iajs-2566 164 14 𝑖𝑓 𝑖𝑓 ADP iajs-2566 164 15 𝛽 𝛽 NOUN iajs-2566 164 16 = = SYM iajs-2566 164 17 𝛼 𝛼 PROPN iajs-2566 164 18 π‘‡β„Žπ‘’π‘› π‘‡β„Žπ‘’π‘› PROPN iajs-2566 164 19 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 164 20 , , PUNCT iajs-2566 164 21 𝛾 𝛾 NOUN iajs-2566 164 22 , , PUNCT iajs-2566 164 23 𝛾 𝛾 NOUN iajs-2566 164 24 ) ) PUNCT iajs-2566 165 1 = = SYM iajs-2566 165 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 165 3 , , PUNCT iajs-2566 165 4 𝛾 𝛾 NOUN iajs-2566 165 5 , , PUNCT iajs-2566 165 6 𝛼 𝛼 NOUN iajs-2566 165 7 ) ) PUNCT iajs-2566 166 1 + + CCONJ iajs-2566 166 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 166 3 , , PUNCT iajs-2566 166 4 𝛾 𝛾 NOUN iajs-2566 166 5 , , PUNCT iajs-2566 166 6 𝛼 𝛼 NOUN iajs-2566 166 7 ) ) PUNCT iajs-2566 166 8 = = SYM iajs-2566 166 9 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 166 10 , , PUNCT iajs-2566 166 11 𝛾 𝛾 NOUN iajs-2566 166 12 , , PUNCT iajs-2566 166 13 𝛼 𝛼 NOUN iajs-2566 166 14 ) ) PUNCT iajs-2566 166 15 β‡’ β‡’ VERB iajs-2566 166 16 𝐷𝑝(𝛾 𝐷𝑝(𝛾 PROPN iajs-2566 166 17 , , PUNCT iajs-2566 166 18 𝛾 𝛾 NOUN iajs-2566 166 19 , , PUNCT iajs-2566 166 20 𝛾 𝛾 NOUN iajs-2566 166 21 ) ) PUNCT iajs-2566 166 22 = = SYM iajs-2566 167 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 167 2 , , PUNCT iajs-2566 167 3 𝛾 𝛾 NOUN iajs-2566 167 4 , , PUNCT iajs-2566 167 5 𝛼 𝛼 NOUN iajs-2566 167 6 ) ) PUNCT iajs-2566 167 7 … … PUNCT iajs-2566 167 8 10 10 NUM iajs-2566 167 9 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 167 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 167 11 ( ( PUNCT iajs-2566 167 12 𝛼 𝛼 PROPN iajs-2566 167 13 , , PUNCT iajs-2566 167 14 𝛼 𝛼 X iajs-2566 167 15 , , PUNCT iajs-2566 167 16 𝛽 𝛽 NOUN iajs-2566 167 17 ) ) PUNCT iajs-2566 167 18 + + PUNCT iajs-2566 168 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 168 2 ( ( PUNCT iajs-2566 168 3 𝛼 𝛼 PROPN iajs-2566 168 4 , , PUNCT iajs-2566 168 5 𝛾 𝛾 NOUN iajs-2566 168 6 , , PUNCT iajs-2566 168 7 𝛾 𝛾 NOUN iajs-2566 168 8 ) ) PUNCT iajs-2566 168 9 βˆ’ βˆ’ NOUN iajs-2566 169 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 169 2 ( ( PUNCT iajs-2566 169 3 𝛼 𝛼 PROPN iajs-2566 169 4 , , PUNCT iajs-2566 169 5 𝛼 𝛼 X iajs-2566 169 6 , , PUNCT iajs-2566 169 7 𝛼 𝛼 NOUN iajs-2566 169 8 ) ) PUNCT iajs-2566 169 9 = = SYM iajs-2566 169 10 0 0 NUM iajs-2566 169 11 β‡’ β‡’ NOUN iajs-2566 169 12 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 169 13 ( ( PUNCT iajs-2566 169 14 𝛼 𝛼 PROPN iajs-2566 169 15 , , PUNCT iajs-2566 169 16 𝛼 𝛼 X iajs-2566 169 17 , , PUNCT iajs-2566 169 18 𝛼 𝛼 NOUN iajs-2566 169 19 ) ) PUNCT iajs-2566 169 20 = = SYM iajs-2566 170 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 170 2 ( ( PUNCT iajs-2566 170 3 𝛼 𝛼 PROPN iajs-2566 170 4 , , PUNCT iajs-2566 170 5 𝛼 𝛼 X iajs-2566 170 6 , , PUNCT iajs-2566 170 7 𝛽 𝛽 NOUN iajs-2566 170 8 ) ) PUNCT iajs-2566 170 9 + + PUNCT iajs-2566 171 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 171 2 ( ( PUNCT iajs-2566 171 3 𝛼 𝛼 PROPN iajs-2566 171 4 , , PUNCT iajs-2566 171 5 𝛾 𝛾 NOUN iajs-2566 171 6 , , PUNCT iajs-2566 171 7 𝛾 𝛾 NOUN iajs-2566 171 8 ) ) PUNCT iajs-2566 171 9 𝑖𝑓 𝑖𝑓 ADP iajs-2566 171 10 𝛽 𝛽 NOUN iajs-2566 171 11 = = SYM iajs-2566 171 12 𝛼 𝛼 PRON iajs-2566 171 13 π‘‡β„Žπ‘’π‘› π‘‡β„Žπ‘’π‘› PROPN iajs-2566 171 14 , , PUNCT iajs-2566 171 15 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 171 16 ( ( PUNCT iajs-2566 171 17 𝛼 𝛼 PROPN iajs-2566 171 18 , , PUNCT iajs-2566 171 19 𝛼 𝛼 X iajs-2566 171 20 , , PUNCT iajs-2566 171 21 𝛼 𝛼 NOUN iajs-2566 171 22 ) ) PUNCT iajs-2566 172 1 = = SYM iajs-2566 172 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 172 3 ( ( PUNCT iajs-2566 172 4 𝛼 𝛼 PROPN iajs-2566 172 5 , , PUNCT iajs-2566 172 6 𝛼 𝛼 X iajs-2566 172 7 , , PUNCT iajs-2566 172 8 𝛼 𝛼 NOUN iajs-2566 172 9 ) ) PUNCT iajs-2566 172 10 + + PUNCT iajs-2566 173 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 173 2 ( ( PUNCT iajs-2566 173 3 𝛼 𝛼 PROPN iajs-2566 173 4 , , PUNCT iajs-2566 173 5 𝛾 𝛾 NOUN iajs-2566 173 6 , , PUNCT iajs-2566 173 7 𝛾 𝛾 NOUN iajs-2566 173 8 ) ) PUNCT iajs-2566 173 9 β‡’ β‡’ NOUN iajs-2566 173 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 173 11 ( ( PUNCT iajs-2566 173 12 𝛼 𝛼 PROPN iajs-2566 173 13 , , PUNCT iajs-2566 173 14 𝛼 𝛼 X iajs-2566 173 15 , , PUNCT iajs-2566 173 16 𝛼 𝛼 NOUN iajs-2566 173 17 ) ) PUNCT iajs-2566 173 18 = = SYM iajs-2566 173 19 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 173 20 , , PUNCT iajs-2566 173 21 𝛾 𝛾 NOUN iajs-2566 173 22 , , PUNCT iajs-2566 173 23 𝛾 𝛾 NOUN iajs-2566 173 24 ) ) PUNCT iajs-2566 173 25 … … PUNCT iajs-2566 173 26 11 11 NUM iajs-2566 173 27 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 173 28 10&11 10&11 NUM iajs-2566 173 29 , , PUNCT iajs-2566 173 30 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 173 31 𝑔𝑒𝑑𝐷𝑝(𝛾 𝑔𝑒𝑑𝐷𝑝(𝛾 PROPN iajs-2566 173 32 , , PUNCT iajs-2566 173 33 𝛾 𝛾 NOUN iajs-2566 173 34 , , PUNCT iajs-2566 173 35 𝛾 𝛾 NOUN iajs-2566 173 36 ) ) PUNCT iajs-2566 173 37 = = SYM iajs-2566 174 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 174 2 , , PUNCT iajs-2566 174 3 𝛾 𝛾 NOUN iajs-2566 174 4 , , PUNCT iajs-2566 174 5 𝛼 𝛼 NOUN iajs-2566 174 6 ) ) PUNCT iajs-2566 174 7 = = SYM iajs-2566 175 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 175 2 , , PUNCT iajs-2566 175 3 𝛼 𝛼 X iajs-2566 175 4 , , PUNCT iajs-2566 175 5 𝛼 𝛼 NOUN iajs-2566 175 6 ) ) PUNCT iajs-2566 175 7 π‘ π‘œ π‘ π‘œ ADP iajs-2566 175 8 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 175 9 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› NOUN iajs-2566 175 10 𝛼 𝛼 NOUN iajs-2566 175 11 = = NOUN iajs-2566 175 12 𝛾 𝛾 PART iajs-2566 175 13 … … PUNCT iajs-2566 175 14 12 12 NUM iajs-2566 175 15 π‘‡β„Žπ‘’π‘› π‘‡β„Žπ‘’π‘› PROPN iajs-2566 175 16 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 175 17 9&12 9&12 NUM iajs-2566 175 18 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 175 19 𝑔𝑒𝑑 𝑔𝑒𝑑 NOUN iajs-2566 175 20 𝛼 𝛼 PROPN iajs-2566 175 21 = = SYM iajs-2566 175 22 𝛽 𝛽 NOUN iajs-2566 175 23 = = SYM iajs-2566 175 24 𝛾. 𝛾. NOUN iajs-2566 175 25 3 3 X iajs-2566 175 26 ) ) PUNCT iajs-2566 175 27 π‘‡π‘Ÿπ‘–π‘£π‘–π‘Žπ‘™ π‘‡π‘Ÿπ‘–π‘£π‘–π‘Žπ‘™ PROPN iajs-2566 175 28 4 4 NUM iajs-2566 175 29 ) ) PUNCT iajs-2566 175 30 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 175 31 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› PROPN iajs-2566 175 32 𝑠𝑖𝑛𝑐𝑒 𝑠𝑖𝑛𝑐𝑒 PROPN iajs-2566 175 33 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ PROPN iajs-2566 175 34 , , PUNCT iajs-2566 175 35 πœ‡ πœ‡ ADP iajs-2566 175 36 , , PUNCT iajs-2566 175 37 𝛽 𝛽 NOUN iajs-2566 175 38 ) ) PUNCT iajs-2566 176 1 + + CCONJ iajs-2566 176 2 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 176 3 , , PUNCT iajs-2566 176 4 πœ‡ πœ‡ X iajs-2566 176 5 , , PUNCT iajs-2566 176 6 𝛾 𝛾 PROPN iajs-2566 176 7 ) ) PUNCT iajs-2566 177 1 βˆ’ βˆ’ PROPN iajs-2566 178 1 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 178 2 , , PUNCT iajs-2566 178 3 πœ‡ πœ‡ X iajs-2566 178 4 , , PUNCT iajs-2566 178 5 πœ‡ πœ‡ NOUN iajs-2566 178 6 ) ) PUNCT iajs-2566 178 7 β‰₯ β‰₯ NOUN iajs-2566 178 8 0 0 NUM iajs-2566 178 9 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 178 10 , , PUNCT iajs-2566 178 11 𝛽 𝛽 NOUN iajs-2566 178 12 , , PUNCT iajs-2566 178 13 πœ‡ πœ‡ ADP iajs-2566 178 14 ) ) PUNCT iajs-2566 178 15 + + NUM iajs-2566 178 16 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 178 17 , , PUNCT iajs-2566 178 18 𝛽 𝛽 NOUN iajs-2566 178 19 , , PUNCT iajs-2566 178 20 πœ‡ πœ‡ ADP iajs-2566 178 21 ) ) PUNCT iajs-2566 178 22 – – PUNCT iajs-2566 178 23 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 178 24 ( ( PUNCT iajs-2566 178 25 𝛽 𝛽 NOUN iajs-2566 178 26 , , PUNCT iajs-2566 178 27 𝛽 𝛽 PROPN iajs-2566 178 28 , , PUNCT iajs-2566 178 29 𝛽 𝛽 PROPN iajs-2566 178 30 ) ) PUNCT iajs-2566 178 31 β‰₯ β‰₯ NOUN iajs-2566 178 32 0 0 NUM iajs-2566 179 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 179 2 , , PUNCT iajs-2566 179 3 𝛾 𝛾 NOUN iajs-2566 179 4 , , PUNCT iajs-2566 179 5 πœ‡ πœ‡ ADP iajs-2566 179 6 ) ) PUNCT iajs-2566 180 1 + + CCONJ iajs-2566 180 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 180 3 , , PUNCT iajs-2566 180 4 𝛾 𝛾 NOUN iajs-2566 180 5 , , PUNCT iajs-2566 180 6 πœ‡ πœ‡ ADP iajs-2566 180 7 ) ) PUNCT iajs-2566 180 8 βˆ’ βˆ’ PROPN iajs-2566 180 9 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 180 10 , , PUNCT iajs-2566 180 11 𝛾 𝛾 NOUN iajs-2566 180 12 , , PUNCT iajs-2566 180 13 𝛾 𝛾 NOUN iajs-2566 180 14 ) ) PUNCT iajs-2566 180 15 β‰₯ β‰₯ NOUN iajs-2566 180 16 0 0 PUNCT iajs-2566 181 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 181 2 ( ( PUNCT iajs-2566 181 3 𝛼 𝛼 INTJ iajs-2566 181 4 , , PUNCT iajs-2566 181 5 𝛼 𝛼 INTJ iajs-2566 181 6 , , PUNCT iajs-2566 181 7 πœ‡ πœ‡ ADP iajs-2566 181 8 ) ) PUNCT iajs-2566 181 9 + + PUNCT iajs-2566 182 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 182 2 ( ( PUNCT iajs-2566 182 3 𝛼 𝛼 INTJ iajs-2566 182 4 , , PUNCT iajs-2566 182 5 𝛼 𝛼 INTJ iajs-2566 182 6 , , PUNCT iajs-2566 182 7 πœ‡ πœ‡ ADP iajs-2566 182 8 ) ) PUNCT iajs-2566 182 9 – – PUNCT iajs-2566 182 10 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 182 11 ( ( PUNCT iajs-2566 182 12 𝛼 𝛼 PROPN iajs-2566 182 13 , , PUNCT iajs-2566 182 14 𝛼 𝛼 INTJ iajs-2566 182 15 , , PUNCT iajs-2566 182 16 𝛼 𝛼 PROPN iajs-2566 182 17 ) ) PUNCT iajs-2566 182 18 β‰₯ β‰₯ NOUN iajs-2566 182 19 0 0 NUM iajs-2566 182 20 , , PUNCT iajs-2566 182 21 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ VERB iajs-2566 182 22 , , PUNCT iajs-2566 182 23 πœ‡ πœ‡ X iajs-2566 182 24 , , PUNCT iajs-2566 182 25 𝛼 𝛼 NOUN iajs-2566 182 26 ) ) PUNCT iajs-2566 182 27 + + CCONJ iajs-2566 182 28 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 182 29 , , PUNCT iajs-2566 182 30 πœ‡ πœ‡ ADP iajs-2566 182 31 , , PUNCT iajs-2566 182 32 𝛾 𝛾 NOUN iajs-2566 182 33 ) ) PUNCT iajs-2566 182 34 – – PUNCT iajs-2566 182 35 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 182 36 , , PUNCT iajs-2566 182 37 πœ‡ πœ‡ X iajs-2566 182 38 , , PUNCT iajs-2566 182 39 πœ‡ πœ‡ NOUN iajs-2566 182 40 ) ) PUNCT iajs-2566 182 41 β‰₯ β‰₯ X iajs-2566 182 42 0 0 NUM iajs-2566 182 43 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ PROPN iajs-2566 182 44 , , PUNCT iajs-2566 182 45 πœ‡ πœ‡ X iajs-2566 182 46 , , PUNCT iajs-2566 182 47 𝛼 𝛼 NOUN iajs-2566 182 48 ) ) PUNCT iajs-2566 182 49 + + CCONJ iajs-2566 182 50 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 182 51 , , PUNCT iajs-2566 182 52 πœ‡ πœ‡ ADP iajs-2566 182 53 , , PUNCT iajs-2566 182 54 𝛽 𝛽 NOUN iajs-2566 182 55 ) ) PUNCT iajs-2566 182 56 – – PUNCT iajs-2566 182 57 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 182 58 , , PUNCT iajs-2566 182 59 πœ‡ πœ‡ X iajs-2566 182 60 , , PUNCT iajs-2566 182 61 πœ‡ πœ‡ NOUN iajs-2566 182 62 ) ) PUNCT iajs-2566 182 63 β‰₯ β‰₯ NOUN iajs-2566 182 64 0 0 NUM iajs-2566 182 65 54 54 NUM iajs-2566 182 66 ibn ibn PROPN iajs-2566 182 67 al al PROPN iajs-2566 182 68 - - PUNCT iajs-2566 182 69 haitham haitham PROPN iajs-2566 182 70 jour jour X iajs-2566 182 71 . . PROPN iajs-2566 183 1 for for ADP iajs-2566 183 2 pure pure ADJ iajs-2566 183 3 & & CCONJ iajs-2566 183 4 appl appl PROPN iajs-2566 183 5 . . PUNCT iajs-2566 184 1 sci sci PROPN iajs-2566 184 2 . . PROPN iajs-2566 185 1 34 34 NUM iajs-2566 185 2 ( ( PUNCT iajs-2566 185 3 1 1 NUM iajs-2566 185 4 ) ) PUNCT iajs-2566 185 5 2021 2021 NUM iajs-2566 185 6 when when SCONJ iajs-2566 185 7 combined combine VERB iajs-2566 185 8 , , PUNCT iajs-2566 185 9 it it PRON iajs-2566 185 10 is be AUX iajs-2566 185 11 more more ADJ iajs-2566 185 12 than than ADP iajs-2566 185 13 and and CCONJ iajs-2566 185 14 equal equal ADJ iajs-2566 185 15 to to ADP iajs-2566 185 16 zero zero NUM iajs-2566 185 17 and and CCONJ iajs-2566 185 18 when when SCONJ iajs-2566 185 19 adding add VERB iajs-2566 185 20 these these DET iajs-2566 185 21 values value NOUN iajs-2566 185 22 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 185 23 ( ( PUNCT iajs-2566 185 24 𝛼 𝛼 INTJ iajs-2566 185 25 , , PUNCT iajs-2566 185 26 𝛼 𝛼 PROPN iajs-2566 185 27 , , PUNCT iajs-2566 185 28 𝛽 𝛽 NOUN iajs-2566 185 29 ) ) PUNCT iajs-2566 185 30 , , PUNCT iajs-2566 185 31 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 185 32 ( ( PUNCT iajs-2566 185 33 𝛼 𝛼 INTJ iajs-2566 185 34 , , PUNCT iajs-2566 185 35 𝛼 𝛼 INTJ iajs-2566 185 36 , , PUNCT iajs-2566 185 37 𝛾 𝛾 PROPN iajs-2566 185 38 ) ) PUNCT iajs-2566 185 39 , , PUNCT iajs-2566 185 40 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 185 41 ( ( PUNCT iajs-2566 185 42 𝛽 𝛽 PROPN iajs-2566 185 43 , , PUNCT iajs-2566 185 44 𝛽 𝛽 PROPN iajs-2566 185 45 , , PUNCT iajs-2566 185 46 𝛼 𝛼 NOUN iajs-2566 185 47 ) ) PUNCT iajs-2566 185 48 , , PUNCT iajs-2566 185 49 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 185 50 ( ( PUNCT iajs-2566 185 51 𝛽 𝛽 PROPN iajs-2566 185 52 , , PUNCT iajs-2566 185 53 𝛽 𝛽 PROPN iajs-2566 185 54 , , PUNCT iajs-2566 185 55 𝛾 𝛾 PROPN iajs-2566 185 56 ) ) PUNCT iajs-2566 185 57 , , PUNCT iajs-2566 185 58 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 185 59 , , PUNCT iajs-2566 185 60 𝛾 𝛾 NOUN iajs-2566 185 61 , , PUNCT iajs-2566 185 62 𝛼 𝛼 NOUN iajs-2566 185 63 ) ) PUNCT iajs-2566 185 64 , , PUNCT iajs-2566 185 65 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 185 66 , , PUNCT iajs-2566 185 67 𝛾 𝛾 NOUN iajs-2566 185 68 , , PUNCT iajs-2566 185 69 𝛽 𝛽 NOUN iajs-2566 185 70 ) ) PUNCT iajs-2566 185 71 , , PUNCT iajs-2566 185 72 βˆ’2𝐷𝑝 βˆ’2𝐷𝑝 NOUN iajs-2566 185 73 ( ( PUNCT iajs-2566 185 74 𝛼 𝛼 X iajs-2566 185 75 , , PUNCT iajs-2566 185 76 𝛼 𝛼 INTJ iajs-2566 185 77 , , PUNCT iajs-2566 185 78 𝛼 𝛼 NOUN iajs-2566 185 79 ) ) PUNCT iajs-2566 185 80 , , PUNCT iajs-2566 185 81 βˆ’2𝐷𝑝 βˆ’2𝐷𝑝 NOUN iajs-2566 185 82 ( ( PUNCT iajs-2566 185 83 𝛽 𝛽 PROPN iajs-2566 185 84 , , PUNCT iajs-2566 185 85 𝛽 𝛽 PROPN iajs-2566 185 86 , , PUNCT iajs-2566 185 87 𝛽 𝛽 NOUN iajs-2566 185 88 ) ) PUNCT iajs-2566 185 89 , , PUNCT iajs-2566 185 90 βˆ’2𝐷𝑝(𝛾 βˆ’2𝐷𝑝(𝛾 NOUN iajs-2566 185 91 , , PUNCT iajs-2566 185 92 𝛾 𝛾 NOUN iajs-2566 185 93 , , PUNCT iajs-2566 185 94 𝛾 𝛾 AUX iajs-2566 185 95 ) ) PUNCT iajs-2566 185 96 π‘‘π‘œ π‘‘π‘œ PROPN iajs-2566 185 97 π‘‘π‘€π‘œ π‘‘π‘€π‘œ VERB iajs-2566 185 98 π‘π‘Žπ‘Ÿπ‘‘π‘–π‘’π‘  π‘π‘Žπ‘Ÿπ‘‘π‘–π‘’π‘  PROPN iajs-2566 185 99 , , PUNCT iajs-2566 185 100 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 185 101 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 185 102 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 185 103 ( ( PUNCT iajs-2566 185 104 𝛼 𝛼 INTJ iajs-2566 185 105 , , PUNCT iajs-2566 185 106 𝛼 𝛼 INTJ iajs-2566 185 107 , , PUNCT iajs-2566 185 108 𝛽 𝛽 NOUN iajs-2566 185 109 ) ) PUNCT iajs-2566 185 110 + + PUNCT iajs-2566 186 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 186 2 ( ( PUNCT iajs-2566 186 3 𝛼 𝛼 INTJ iajs-2566 186 4 , , PUNCT iajs-2566 186 5 𝛼 𝛼 INTJ iajs-2566 186 6 , , PUNCT iajs-2566 186 7 𝛾 𝛾 NOUN iajs-2566 186 8 ) ) PUNCT iajs-2566 186 9 + + PUNCT iajs-2566 187 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 187 2 ( ( PUNCT iajs-2566 187 3 𝛽 𝛽 PROPN iajs-2566 187 4 , , PUNCT iajs-2566 187 5 𝛽 𝛽 PROPN iajs-2566 187 6 , , PUNCT iajs-2566 187 7 𝛼 𝛼 PROPN iajs-2566 187 8 ) ) PUNCT iajs-2566 187 9 + + PUNCT iajs-2566 188 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 188 2 ( ( PUNCT iajs-2566 188 3 𝛽 𝛽 PROPN iajs-2566 188 4 , , PUNCT iajs-2566 188 5 𝛽 𝛽 PROPN iajs-2566 188 6 , , PUNCT iajs-2566 188 7 𝛾 𝛾 PROPN iajs-2566 188 8 ) ) PUNCT iajs-2566 189 1 + + CCONJ iajs-2566 189 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 189 3 , , PUNCT iajs-2566 189 4 𝛾 𝛾 NOUN iajs-2566 189 5 , , PUNCT iajs-2566 189 6 𝛼 𝛼 NOUN iajs-2566 189 7 ) ) PUNCT iajs-2566 190 1 + + CCONJ iajs-2566 190 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 190 3 , , PUNCT iajs-2566 190 4 𝛾 𝛾 NOUN iajs-2566 190 5 , , PUNCT iajs-2566 190 6 𝛽 𝛽 NOUN iajs-2566 190 7 ) ) PUNCT iajs-2566 190 8 – – PUNCT iajs-2566 190 9 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 190 10 ( ( PUNCT iajs-2566 190 11 𝛼 𝛼 PROPN iajs-2566 190 12 , , PUNCT iajs-2566 190 13 𝛼 𝛼 INTJ iajs-2566 190 14 , , PUNCT iajs-2566 190 15 𝛼 𝛼 NOUN iajs-2566 190 16 ) ) PUNCT iajs-2566 190 17 – – PUNCT iajs-2566 190 18 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 190 19 ( ( PUNCT iajs-2566 190 20 𝛽 𝛽 NOUN iajs-2566 190 21 , , PUNCT iajs-2566 190 22 𝛽 𝛽 PROPN iajs-2566 190 23 , , PUNCT iajs-2566 190 24 𝛽 𝛽 PROPN iajs-2566 190 25 ) ) PUNCT iajs-2566 190 26 – – PUNCT iajs-2566 190 27 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 190 28 , , PUNCT iajs-2566 190 29 𝛾 𝛾 NOUN iajs-2566 190 30 , , PUNCT iajs-2566 190 31 𝛾 𝛾 NOUN iajs-2566 190 32 ) ) PUNCT iajs-2566 190 33 ≀ ≀ PUNCT iajs-2566 191 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 191 2 ( ( PUNCT iajs-2566 191 3 𝛼 𝛼 INTJ iajs-2566 191 4 , , PUNCT iajs-2566 191 5 𝛼 𝛼 INTJ iajs-2566 191 6 , , PUNCT iajs-2566 191 7 𝛽 𝛽 NOUN iajs-2566 191 8 ) ) PUNCT iajs-2566 191 9 + + PUNCT iajs-2566 192 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 192 2 ( ( PUNCT iajs-2566 192 3 𝛼 𝛼 INTJ iajs-2566 192 4 , , PUNCT iajs-2566 192 5 𝛼 𝛼 INTJ iajs-2566 192 6 , , PUNCT iajs-2566 192 7 𝛾 𝛾 NOUN iajs-2566 192 8 ) ) PUNCT iajs-2566 192 9 + + PUNCT iajs-2566 193 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 193 2 ( ( PUNCT iajs-2566 193 3 𝛽 𝛽 PROPN iajs-2566 193 4 , , PUNCT iajs-2566 193 5 𝛽 𝛽 PROPN iajs-2566 193 6 , , PUNCT iajs-2566 193 7 𝛼 𝛼 PROPN iajs-2566 193 8 ) ) PUNCT iajs-2566 193 9 + + PUNCT iajs-2566 194 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 194 2 ( ( PUNCT iajs-2566 194 3 𝛽 𝛽 PROPN iajs-2566 194 4 , , PUNCT iajs-2566 194 5 𝛽 𝛽 PROPN iajs-2566 194 6 , , PUNCT iajs-2566 194 7 𝛾 𝛾 PROPN iajs-2566 194 8 ) ) PUNCT iajs-2566 195 1 + + CCONJ iajs-2566 195 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 195 3 , , PUNCT iajs-2566 195 4 𝛾 𝛾 NOUN iajs-2566 195 5 , , PUNCT iajs-2566 195 6 𝛼 𝛼 ADJ iajs-2566 195 7 ) ) PUNCT iajs-2566 196 1 + + CCONJ iajs-2566 196 2 𝐷𝑝𝛾 𝐷𝑝𝛾 PROPN iajs-2566 196 3 , , PUNCT iajs-2566 196 4 𝛾 𝛾 NOUN iajs-2566 196 5 , , PUNCT iajs-2566 196 6 𝛽 𝛽 NOUN iajs-2566 196 7 ) ) PUNCT iajs-2566 196 8 – – PUNCT iajs-2566 196 9 2𝐷𝑝(𝛼 2𝐷𝑝(𝛼 NUM iajs-2566 196 10 , , PUNCT iajs-2566 196 11 𝛼 𝛼 INTJ iajs-2566 196 12 , , PUNCT iajs-2566 196 13 𝛼 𝛼 NOUN iajs-2566 196 14 ) ) PUNCT iajs-2566 196 15 – – PUNCT iajs-2566 196 16 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 196 17 ( ( PUNCT iajs-2566 196 18 𝛽 𝛽 NOUN iajs-2566 196 19 , , PUNCT iajs-2566 196 20 𝛽 𝛽 PROPN iajs-2566 196 21 , , PUNCT iajs-2566 196 22 𝛽 𝛽 PROPN iajs-2566 196 23 ) ) PUNCT iajs-2566 196 24 βˆ’ βˆ’ PROPN iajs-2566 196 25 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 PROPN iajs-2566 196 26 , , PUNCT iajs-2566 196 27 𝛾 𝛾 X iajs-2566 196 28 , , PUNCT iajs-2566 196 29 𝛾 𝛾 NOUN iajs-2566 196 30 ) ) PUNCT iajs-2566 196 31 + + CCONJ iajs-2566 196 32 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 196 33 , , PUNCT iajs-2566 196 34 πœ‡ πœ‡ ADP iajs-2566 196 35 , , PUNCT iajs-2566 196 36 𝛽 𝛽 NOUN iajs-2566 196 37 ) ) PUNCT iajs-2566 197 1 + + CCONJ iajs-2566 197 2 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 197 3 , , PUNCT iajs-2566 197 4 πœ‡ πœ‡ X iajs-2566 197 5 , , PUNCT iajs-2566 197 6 𝛾 𝛾 NOUN iajs-2566 197 7 ) ) PUNCT iajs-2566 197 8 + + NUM iajs-2566 197 9 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 197 10 , , PUNCT iajs-2566 197 11 𝛽 𝛽 NOUN iajs-2566 197 12 , , PUNCT iajs-2566 197 13 πœ‡ πœ‡ ADP iajs-2566 197 14 ) ) PUNCT iajs-2566 197 15 + + PUNCT iajs-2566 198 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 198 2 ( ( PUNCT iajs-2566 198 3 𝛽 𝛽 PROPN iajs-2566 198 4 , , PUNCT iajs-2566 198 5 𝛽 𝛽 PROPN iajs-2566 198 6 , , PUNCT iajs-2566 198 7 πœ‡ πœ‡ ADP iajs-2566 198 8 ) ) PUNCT iajs-2566 198 9 + + CCONJ iajs-2566 198 10 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 198 11 , , PUNCT iajs-2566 198 12 𝛾 𝛾 NOUN iajs-2566 198 13 , , PUNCT iajs-2566 198 14 πœ‡ πœ‡ ADP iajs-2566 198 15 ) ) PUNCT iajs-2566 198 16 + + CCONJ iajs-2566 198 17 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 198 18 , , PUNCT iajs-2566 198 19 𝛾 𝛾 NOUN iajs-2566 198 20 , , PUNCT iajs-2566 198 21 πœ‡ πœ‡ ADP iajs-2566 198 22 ) ) PUNCT iajs-2566 198 23 + + PUNCT iajs-2566 199 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 199 2 ( ( PUNCT iajs-2566 199 3 𝛼 𝛼 INTJ iajs-2566 199 4 , , PUNCT iajs-2566 199 5 𝛼 𝛼 INTJ iajs-2566 199 6 , , PUNCT iajs-2566 199 7 πœ‡ πœ‡ ADP iajs-2566 199 8 ) ) PUNCT iajs-2566 199 9 + + CCONJ iajs-2566 199 10 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 199 11 , , PUNCT iajs-2566 199 12 𝛼 𝛼 INTJ iajs-2566 199 13 , , PUNCT iajs-2566 199 14 πœ‡ πœ‡ ADP iajs-2566 199 15 ) ) PUNCT iajs-2566 199 16 + + CCONJ iajs-2566 199 17 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 199 18 , , PUNCT iajs-2566 199 19 πœ‡ πœ‡ X iajs-2566 199 20 , , PUNCT iajs-2566 199 21 𝛼 𝛼 NOUN iajs-2566 199 22 ) ) PUNCT iajs-2566 199 23 + + CCONJ iajs-2566 199 24 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 199 25 , , PUNCT iajs-2566 199 26 πœ‡ πœ‡ X iajs-2566 199 27 , , PUNCT iajs-2566 199 28 𝛾 𝛾 NOUN iajs-2566 199 29 ) ) PUNCT iajs-2566 200 1 + + CCONJ iajs-2566 200 2 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 200 3 , , PUNCT iajs-2566 200 4 πœ‡ πœ‡ X iajs-2566 200 5 , , PUNCT iajs-2566 200 6 𝛼 𝛼 NOUN iajs-2566 200 7 ) ) PUNCT iajs-2566 200 8 + + CCONJ iajs-2566 200 9 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 200 10 , , PUNCT iajs-2566 200 11 πœ‡ πœ‡ ADP iajs-2566 200 12 , , PUNCT iajs-2566 200 13 𝛽 𝛽 NOUN iajs-2566 200 14 ) ) PUNCT iajs-2566 200 15 – – PUNCT iajs-2566 200 16 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 200 17 , , PUNCT iajs-2566 200 18 πœ‡ πœ‡ X iajs-2566 200 19 , , PUNCT iajs-2566 200 20 πœ‡ πœ‡ NOUN iajs-2566 200 21 ) ) PUNCT iajs-2566 200 22 – – PUNCT iajs-2566 200 23 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 200 24 ( ( PUNCT iajs-2566 200 25 𝛽 𝛽 NOUN iajs-2566 200 26 , , PUNCT iajs-2566 200 27 𝛽 𝛽 PROPN iajs-2566 200 28 , , PUNCT iajs-2566 200 29 𝛽 𝛽 PROPN iajs-2566 200 30 ) ) PUNCT iajs-2566 200 31 – – PUNCT iajs-2566 200 32 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 200 33 , , PUNCT iajs-2566 200 34 𝛾 𝛾 NOUN iajs-2566 200 35 , , PUNCT iajs-2566 200 36 𝛾 𝛾 NOUN iajs-2566 200 37 ) ) PUNCT iajs-2566 200 38 – – PUNCT iajs-2566 200 39 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 200 40 ( ( PUNCT iajs-2566 200 41 𝛼 𝛼 PROPN iajs-2566 200 42 , , PUNCT iajs-2566 200 43 𝛼 𝛼 INTJ iajs-2566 200 44 , , PUNCT iajs-2566 200 45 𝛼 𝛼 NOUN iajs-2566 200 46 ) ) PUNCT iajs-2566 200 47 – – PUNCT iajs-2566 200 48 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 200 49 , , PUNCT iajs-2566 200 50 πœ‡ πœ‡ X iajs-2566 200 51 , , PUNCT iajs-2566 200 52 πœ‡ πœ‡ NOUN iajs-2566 200 53 ) ) PUNCT iajs-2566 200 54 – – PUNCT iajs-2566 200 55 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 200 56 , , PUNCT iajs-2566 200 57 πœ‡ πœ‡ X iajs-2566 200 58 , , PUNCT iajs-2566 200 59 πœ‡ πœ‡ ADP iajs-2566 200 60 ) ) PUNCT iajs-2566 200 61 = = NOUN iajs-2566 201 1 [ [ X iajs-2566 201 2 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 201 3 , , PUNCT iajs-2566 201 4 πœ‡ πœ‡ ADP iajs-2566 201 5 , , PUNCT iajs-2566 201 6 𝛽 𝛽 NOUN iajs-2566 201 7 ) ) PUNCT iajs-2566 201 8 + + CCONJ iajs-2566 201 9 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 201 10 , , PUNCT iajs-2566 201 11 πœ‡ πœ‡ X iajs-2566 201 12 , , PUNCT iajs-2566 201 13 𝛾 𝛾 PROPN iajs-2566 201 14 ) ) PUNCT iajs-2566 201 15 + + PUNCT iajs-2566 202 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 202 2 ( ( PUNCT iajs-2566 202 3 𝛽 𝛽 PROPN iajs-2566 202 4 , , PUNCT iajs-2566 202 5 𝛽 𝛽 PROPN iajs-2566 202 6 , , PUNCT iajs-2566 202 7 πœ‡ πœ‡ ADP iajs-2566 202 8 ) ) PUNCT iajs-2566 202 9 + + PUNCT iajs-2566 203 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 203 2 ( ( PUNCT iajs-2566 203 3 𝛽 𝛽 PROPN iajs-2566 203 4 , , PUNCT iajs-2566 203 5 𝛽 𝛽 PROPN iajs-2566 203 6 , , PUNCT iajs-2566 203 7 𝛾 𝛾 PROPN iajs-2566 203 8 ) ) PUNCT iajs-2566 204 1 + + CCONJ iajs-2566 204 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 204 3 , , PUNCT iajs-2566 204 4 𝛾 𝛾 NOUN iajs-2566 204 5 , , PUNCT iajs-2566 204 6 πœ‡ πœ‡ ADP iajs-2566 204 7 ) ) PUNCT iajs-2566 205 1 + + CCONJ iajs-2566 205 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 205 3 , , PUNCT iajs-2566 205 4 𝛾 𝛾 NOUN iajs-2566 205 5 , , PUNCT iajs-2566 205 6 𝛽 𝛽 NOUN iajs-2566 205 7 ) ) PUNCT iajs-2566 205 8 – – PUNCT iajs-2566 205 9 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 205 10 , , PUNCT iajs-2566 205 11 πœ‡ πœ‡ ADP iajs-2566 205 12 , , PUNCT iajs-2566 205 13 πœ‡ πœ‡ NOUN iajs-2566 205 14 ) ) PUNCT iajs-2566 205 15 – – PUNCT iajs-2566 205 16 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 205 17 ( ( PUNCT iajs-2566 205 18 𝛽 𝛽 NOUN iajs-2566 205 19 , , PUNCT iajs-2566 205 20 𝛽 𝛽 PROPN iajs-2566 205 21 , , PUNCT iajs-2566 205 22 𝛽 𝛽 NOUN iajs-2566 205 23 ) ) PUNCT iajs-2566 205 24 – – PUNCT iajs-2566 205 25 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 205 26 , , PUNCT iajs-2566 205 27 𝛾 𝛾 NOUN iajs-2566 205 28 , , PUNCT iajs-2566 205 29 𝛾 𝛾 NOUN iajs-2566 205 30 ) ) PUNCT iajs-2566 205 31 ] ] PUNCT iajs-2566 206 1 + + CCONJ iajs-2566 207 1 [ [ X iajs-2566 207 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 207 3 ( ( PUNCT iajs-2566 207 4 𝛼 𝛼 INTJ iajs-2566 207 5 , , PUNCT iajs-2566 207 6 𝛼 𝛼 X iajs-2566 207 7 , , PUNCT iajs-2566 207 8 πœ‡ πœ‡ ADP iajs-2566 207 9 ) ) PUNCT iajs-2566 207 10 + + PUNCT iajs-2566 208 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 208 2 ( ( PUNCT iajs-2566 208 3 𝛼 𝛼 INTJ iajs-2566 208 4 , , PUNCT iajs-2566 208 5 𝛼 𝛼 INTJ iajs-2566 208 6 , , PUNCT iajs-2566 208 7 𝛾 𝛾 PROPN iajs-2566 208 8 ) ) PUNCT iajs-2566 208 9 + + CCONJ iajs-2566 208 10 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 208 11 , , PUNCT iajs-2566 208 12 πœ‡ πœ‡ X iajs-2566 208 13 , , PUNCT iajs-2566 208 14 𝛼 𝛼 NOUN iajs-2566 208 15 ) ) PUNCT iajs-2566 208 16 + + CCONJ iajs-2566 208 17 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ PROPN iajs-2566 208 18 , , PUNCT iajs-2566 208 19 πœ‡ πœ‡ X iajs-2566 208 20 , , PUNCT iajs-2566 208 21 𝛾 𝛾 NOUN iajs-2566 208 22 ) ) PUNCT iajs-2566 209 1 + + CCONJ iajs-2566 209 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 209 3 , , PUNCT iajs-2566 209 4 𝛾 𝛾 NOUN iajs-2566 209 5 , , PUNCT iajs-2566 209 6 𝛼 𝛼 NOUN iajs-2566 209 7 ) ) PUNCT iajs-2566 210 1 + + CCONJ iajs-2566 210 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 210 3 , , PUNCT iajs-2566 210 4 𝛾 𝛾 NOUN iajs-2566 210 5 , , PUNCT iajs-2566 210 6 πœ‡ πœ‡ ADP iajs-2566 210 7 ) ) PUNCT iajs-2566 210 8 – – PUNCT iajs-2566 210 9 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 210 10 ( ( PUNCT iajs-2566 210 11 𝛼 𝛼 X iajs-2566 210 12 , , PUNCT iajs-2566 210 13 𝛼 𝛼 X iajs-2566 210 14 , , PUNCT iajs-2566 210 15 𝛼 𝛼 NOUN iajs-2566 210 16 ) ) PUNCT iajs-2566 210 17 – – PUNCT iajs-2566 210 18 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 210 19 , , PUNCT iajs-2566 210 20 πœ‡ πœ‡ X iajs-2566 210 21 , , PUNCT iajs-2566 210 22 πœ‡ πœ‡ NOUN iajs-2566 210 23 ) ) PUNCT iajs-2566 210 24 – – PUNCT iajs-2566 210 25 2𝐷𝑝(𝛾 2𝐷𝑝(𝛾 NUM iajs-2566 210 26 , , PUNCT iajs-2566 210 27 𝛾 𝛾 NOUN iajs-2566 210 28 , , PUNCT iajs-2566 210 29 𝛾 𝛾 NOUN iajs-2566 210 30 ) ) PUNCT iajs-2566 210 31 ] ] PUNCT iajs-2566 211 1 + + CCONJ iajs-2566 212 1 [ [ X iajs-2566 212 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 212 3 ( ( PUNCT iajs-2566 212 4 𝛼 𝛼 INTJ iajs-2566 212 5 , , PUNCT iajs-2566 212 6 𝛼 𝛼 PROPN iajs-2566 212 7 , , PUNCT iajs-2566 212 8 𝛽 𝛽 NOUN iajs-2566 212 9 ) ) PUNCT iajs-2566 212 10 + + PUNCT iajs-2566 213 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 213 2 ( ( PUNCT iajs-2566 213 3 𝛼 𝛼 INTJ iajs-2566 213 4 , , PUNCT iajs-2566 213 5 𝛼 𝛼 INTJ iajs-2566 213 6 , , PUNCT iajs-2566 213 7 πœ‡ πœ‡ ADP iajs-2566 213 8 ) ) PUNCT iajs-2566 213 9 + + PUNCT iajs-2566 214 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 214 2 ( ( PUNCT iajs-2566 214 3 𝛽 𝛽 PROPN iajs-2566 214 4 , , PUNCT iajs-2566 214 5 𝛽 𝛽 PROPN iajs-2566 214 6 , , PUNCT iajs-2566 214 7 𝛼 𝛼 PROPN iajs-2566 214 8 ) ) PUNCT iajs-2566 214 9 + + NUM iajs-2566 214 10 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 214 11 , , PUNCT iajs-2566 214 12 𝛽 𝛽 NOUN iajs-2566 214 13 , , PUNCT iajs-2566 214 14 πœ‡ πœ‡ ADP iajs-2566 214 15 ) ) PUNCT iajs-2566 214 16 + + CCONJ iajs-2566 214 17 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 214 18 , , PUNCT iajs-2566 214 19 πœ‡ πœ‡ X iajs-2566 214 20 , , PUNCT iajs-2566 214 21 𝛼 𝛼 NOUN iajs-2566 214 22 ) ) PUNCT iajs-2566 214 23 + + CCONJ iajs-2566 214 24 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ X iajs-2566 214 25 , , PUNCT iajs-2566 214 26 πœ‡ πœ‡ ADP iajs-2566 214 27 , , PUNCT iajs-2566 214 28 𝛽 𝛽 NOUN iajs-2566 214 29 ) ) PUNCT iajs-2566 214 30 – – PUNCT iajs-2566 214 31 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 214 32 ( ( PUNCT iajs-2566 214 33 𝛼 𝛼 X iajs-2566 214 34 , , PUNCT iajs-2566 214 35 𝛼 𝛼 X iajs-2566 214 36 , , PUNCT iajs-2566 214 37 𝛼 𝛼 NOUN iajs-2566 214 38 ) ) PUNCT iajs-2566 214 39 – – PUNCT iajs-2566 214 40 2𝐷𝑝(𝛽 2𝐷𝑝(𝛽 NUM iajs-2566 214 41 , , PUNCT iajs-2566 214 42 𝛽 𝛽 NOUN iajs-2566 214 43 , , PUNCT iajs-2566 214 44 𝛽 𝛽 NOUN iajs-2566 214 45 ) ) PUNCT iajs-2566 214 46 – – PUNCT iajs-2566 214 47 2𝐷𝑝(πœ‡ 2𝐷𝑝(πœ‡ NUM iajs-2566 214 48 , , PUNCT iajs-2566 214 49 πœ‡ πœ‡ X iajs-2566 214 50 , , PUNCT iajs-2566 214 51 πœ‡ πœ‡ NOUN iajs-2566 214 52 ) ) PUNCT iajs-2566 214 53 ] ] PUNCT iajs-2566 214 54 β‡’ β‡’ PROPN iajs-2566 214 55 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 214 56 ( ( PUNCT iajs-2566 214 57 𝛼 𝛼 INTJ iajs-2566 214 58 , , PUNCT iajs-2566 214 59 𝛽 𝛽 NOUN iajs-2566 214 60 , , PUNCT iajs-2566 214 61 𝛾 𝛾 NOUN iajs-2566 214 62 ) ) PUNCT iajs-2566 214 63 ≀ ≀ NOUN iajs-2566 214 64 𝐷𝑔(πœ‡ 𝐷𝑔(πœ‡ ADJ iajs-2566 214 65 , , PUNCT iajs-2566 214 66 𝛽 𝛽 PROPN iajs-2566 214 67 , , PUNCT iajs-2566 214 68 𝛾 𝛾 PROPN iajs-2566 214 69 ) ) PUNCT iajs-2566 214 70 + + CCONJ iajs-2566 214 71 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 214 72 ( ( PUNCT iajs-2566 214 73 𝛼 𝛼 INTJ iajs-2566 214 74 , , PUNCT iajs-2566 214 75 πœ‡ πœ‡ ADP iajs-2566 214 76 , , PUNCT iajs-2566 214 77 𝛾 𝛾 NOUN iajs-2566 214 78 ) ) PUNCT iajs-2566 214 79 + + CCONJ iajs-2566 214 80 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 214 81 ( ( PUNCT iajs-2566 214 82 𝛼 𝛼 INTJ iajs-2566 214 83 , , PUNCT iajs-2566 214 84 𝛽 𝛽 PROPN iajs-2566 214 85 , , PUNCT iajs-2566 214 86 πœ‡ πœ‡ ADP iajs-2566 214 87 ) ) PUNCT iajs-2566 214 88 βŽ• βŽ• VERB iajs-2566 214 89 corollary corollary ADJ iajs-2566 214 90 13 13 NUM iajs-2566 214 91 let let NOUN iajs-2566 214 92 ( ( PUNCT iajs-2566 214 93 π‘Œ π‘Œ PROPN iajs-2566 214 94 , , PUNCT iajs-2566 214 95 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 214 96 ) ) PUNCT iajs-2566 214 97 be be VERB iajs-2566 214 98 a a DET iajs-2566 214 99 general general ADJ iajs-2566 214 100 partial partial ADJ iajs-2566 214 101 metric metric ADJ iajs-2566 214 102 space space NOUN iajs-2566 214 103 , , PUNCT iajs-2566 214 104 the the DET iajs-2566 214 105 function function NOUN iajs-2566 214 106 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 214 107 : : PUNCT iajs-2566 215 1 π‘Œ3 π‘Œ3 PROPN iajs-2566 215 2 ⟢ ⟢ PROPN iajs-2566 215 3 [ [ X iajs-2566 215 4 0 0 NUM iajs-2566 215 5 , , PUNCT iajs-2566 215 6 ∞ ∞ NOUN iajs-2566 215 7 ) ) PUNCT iajs-2566 215 8 given give VERB iajs-2566 215 9 by by ADP iajs-2566 215 10 𝐷𝑔(𝛼 𝐷𝑔(𝛼 PROPN iajs-2566 215 11 , , PUNCT iajs-2566 215 12 𝛽 𝛽 NOUN iajs-2566 215 13 , , PUNCT iajs-2566 215 14 𝛾 𝛾 NOUN iajs-2566 215 15 ) ) PUNCT iajs-2566 216 1 = = SYM iajs-2566 216 2 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 216 3 , , PUNCT iajs-2566 216 4 𝛽 𝛽 NOUN iajs-2566 216 5 , , PUNCT iajs-2566 216 6 𝛾 𝛾 NOUN iajs-2566 216 7 ) ) PUNCT iajs-2566 216 8 + + CCONJ iajs-2566 216 9 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 216 10 , , PUNCT iajs-2566 216 11 𝛼 𝛼 X iajs-2566 216 12 , , PUNCT iajs-2566 216 13 𝛽 𝛽 NOUN iajs-2566 216 14 ) ) PUNCT iajs-2566 216 15 + + CCONJ iajs-2566 216 16 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 216 17 , , PUNCT iajs-2566 216 18 𝛼 𝛼 NOUN iajs-2566 216 19 , , PUNCT iajs-2566 216 20 𝛾 𝛾 NOUN iajs-2566 216 21 ) ) PUNCT iajs-2566 216 22 + + NUM iajs-2566 216 23 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 216 24 , , PUNCT iajs-2566 216 25 𝛽 𝛽 NOUN iajs-2566 216 26 , , PUNCT iajs-2566 216 27 𝛼 𝛼 NOUN iajs-2566 216 28 ) ) PUNCT iajs-2566 216 29 + + PUNCT iajs-2566 217 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 217 2 ( ( PUNCT iajs-2566 217 3 𝛽 𝛽 PROPN iajs-2566 217 4 , , PUNCT iajs-2566 217 5 𝛽 𝛽 NOUN iajs-2566 217 6 , , PUNCT iajs-2566 217 7 𝛾 𝛾 NOUN iajs-2566 217 8 ) ) PUNCT iajs-2566 218 1 + + CCONJ iajs-2566 218 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 218 3 , , PUNCT iajs-2566 218 4 𝛾 𝛾 NOUN iajs-2566 218 5 , , PUNCT iajs-2566 218 6 𝛼 𝛼 NOUN iajs-2566 218 7 ) ) PUNCT iajs-2566 218 8 + + CCONJ iajs-2566 218 9 𝐷𝑝(𝛾 𝐷𝑝(𝛾 ADJ iajs-2566 218 10 , , PUNCT iajs-2566 218 11 𝛾 𝛾 NOUN iajs-2566 218 12 , , PUNCT iajs-2566 218 13 𝛽 𝛽 NOUN iajs-2566 218 14 ) ) PUNCT iajs-2566 218 15 βˆ’ βˆ’ PROPN iajs-2566 219 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 219 2 ( ( PUNCT iajs-2566 219 3 𝛼 𝛼 PROPN iajs-2566 219 4 , , PUNCT iajs-2566 219 5 𝛼 𝛼 X iajs-2566 219 6 , , PUNCT iajs-2566 219 7 𝛼 𝛼 NOUN iajs-2566 219 8 ) ) PUNCT iajs-2566 219 9 βˆ’ βˆ’ ADP iajs-2566 220 1 2𝐷𝑝 2𝐷𝑝 NUM iajs-2566 220 2 ( ( PUNCT iajs-2566 220 3 𝛽 𝛽 PROPN iajs-2566 220 4 , , PUNCT iajs-2566 220 5 𝛽 𝛽 PROPN iajs-2566 220 6 , , PUNCT iajs-2566 220 7 𝛽 𝛽 NOUN iajs-2566 220 8 ) ) PUNCT iajs-2566 220 9 βˆ’ βˆ’ PROPN iajs-2566 221 1 3𝐷𝑝(𝛾 3𝐷𝑝(𝛾 NUM iajs-2566 221 2 , , PUNCT iajs-2566 221 3 𝛾 𝛾 NOUN iajs-2566 221 4 , , PUNCT iajs-2566 221 5 𝛾 𝛾 NOUN iajs-2566 221 6 ) ) PUNCT iajs-2566 221 7 𝑖𝑠 𝑖𝑠 NOUN iajs-2566 222 1 𝐷 𝐷 NOUN iajs-2566 222 2 βˆ’ βˆ’ NOUN iajs-2566 222 3 π‘šπ‘’π‘‘π‘Ÿπ‘–π‘ π‘šπ‘’π‘‘π‘Ÿπ‘–π‘ NOUN iajs-2566 222 4 π‘ π‘π‘Žπ‘π‘’. π‘ π‘π‘Žπ‘π‘’. NOUN iajs-2566 222 5 ( ( PUNCT iajs-2566 222 6 1.2 1.2 NUM iajs-2566 222 7 ) ) PUNCT iajs-2566 222 8 proof proof NOUN iajs-2566 222 9 : : PUNCT iajs-2566 222 10 the the DET iajs-2566 222 11 prove prove NOUN iajs-2566 222 12 is be AUX iajs-2566 222 13 similar similar ADJ iajs-2566 222 14 to to AUX iajs-2566 222 15 theorem theorem VERB iajs-2566 222 16 12 12 NUM iajs-2566 222 17 remark remark NOUN iajs-2566 222 18 14 14 NUM iajs-2566 222 19 it it PRON iajs-2566 222 20 is be AUX iajs-2566 222 21 clear clear ADJ iajs-2566 222 22 from from ADP iajs-2566 222 23 definition definition NOUN iajs-2566 222 24 that that SCONJ iajs-2566 222 25 every every DET iajs-2566 222 26 d d ADJ iajs-2566 222 27 - - ADJ iajs-2566 222 28 metric metric ADJ iajs-2566 222 29 space space NOUN iajs-2566 222 30 ( ( PUNCT iajs-2566 222 31 π‘Œ π‘Œ PROPN iajs-2566 222 32 , , PUNCT iajs-2566 222 33 𝐷 𝐷 PROPN iajs-2566 222 34 ) ) PUNCT iajs-2566 222 35 is be AUX iajs-2566 222 36 a a DET iajs-2566 222 37 general general ADJ iajs-2566 222 38 partial partial ADJ iajs-2566 222 39 metric metric ADJ iajs-2566 222 40 space(π‘Œ space(π‘Œ NOUN iajs-2566 222 41 , , PUNCT iajs-2566 222 42 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 222 43 ) ) PUNCT iajs-2566 222 44 , , PUNCT iajs-2566 222 45 but but CCONJ iajs-2566 222 46 the the DET iajs-2566 222 47 converse converse NOUN iajs-2566 222 48 is be AUX iajs-2566 222 49 not not PART iajs-2566 222 50 true true ADJ iajs-2566 222 51 . . PUNCT iajs-2566 223 1 as as SCONJ iajs-2566 223 2 we we PRON iajs-2566 223 3 saw see VERB iajs-2566 223 4 in in ADP iajs-2566 223 5 example example NOUN iajs-2566 223 6 2 2 NUM iajs-2566 223 7 , , PUNCT iajs-2566 223 8 by by ADP iajs-2566 223 9 definition definition NOUN iajs-2566 223 10 of of ADP iajs-2566 223 11 d d ADJ iajs-2566 223 12 - - ADJ iajs-2566 223 13 metric metric ADJ iajs-2566 223 14 space space NOUN iajs-2566 223 15 if if SCONJ iajs-2566 223 16 𝛼 𝛼 PROPN iajs-2566 223 17 = = SYM iajs-2566 223 18 𝛽 𝛽 NOUN iajs-2566 223 19 = = SYM iajs-2566 223 20 𝛾 𝛾 PROPN iajs-2566 223 21 then then ADV iajs-2566 223 22 𝐷(𝛼 𝐷(𝛼 VERB iajs-2566 223 23 , , PUNCT iajs-2566 223 24 𝛽 𝛽 NOUN iajs-2566 223 25 , , PUNCT iajs-2566 223 26 𝛾 𝛾 NOUN iajs-2566 223 27 ) ) PUNCT iajs-2566 223 28 = = SYM iajs-2566 223 29 0 0 PUNCT iajs-2566 223 30 suppose suppose VERB iajs-2566 223 31 𝛼 𝛼 X iajs-2566 223 32 = = SYM iajs-2566 223 33 5 5 NUM iajs-2566 223 34 = = SYM iajs-2566 223 35 𝛽 𝛽 NOUN iajs-2566 223 36 = = SYM iajs-2566 223 37 𝛾 𝛾 PROPN iajs-2566 223 38 then then ADV iajs-2566 223 39 𝐷𝑝(5 𝐷𝑝(5 PROPN iajs-2566 223 40 , , PUNCT iajs-2566 223 41 5 5 NUM iajs-2566 223 42 , , PUNCT iajs-2566 223 43 5 5 NUM iajs-2566 223 44 ) ) PUNCT iajs-2566 223 45 = = SYM iajs-2566 223 46 π‘šπ‘Žπ›Ό{5 π‘šπ‘Žπ›Ό{5 NOUN iajs-2566 223 47 , , PUNCT iajs-2566 223 48 5 5 NUM iajs-2566 223 49 , , PUNCT iajs-2566 223 50 5 5 NUM iajs-2566 223 51 } } PUNCT iajs-2566 223 52 = = SYM iajs-2566 223 53 5 5 NUM iajs-2566 223 54 β‰  β‰  PROPN iajs-2566 223 55 0 0 NUM iajs-2566 223 56 lemma lemma PROPN iajs-2566 223 57 15 15 NUM iajs-2566 223 58 let let NOUN iajs-2566 223 59 ( ( PUNCT iajs-2566 223 60 π‘Œ π‘Œ PROPN iajs-2566 223 61 , , PUNCT iajs-2566 223 62 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 223 63 ) ) PUNCT iajs-2566 223 64 be be VERB iajs-2566 223 65 a a DET iajs-2566 223 66 general general ADJ iajs-2566 223 67 partial partial ADJ iajs-2566 223 68 metric metric ADJ iajs-2566 223 69 space space NOUN iajs-2566 223 70 if if SCONJ iajs-2566 223 71 { { PUNCT iajs-2566 223 72 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š NOUN iajs-2566 223 73 , , PUNCT iajs-2566 223 74 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 223 75 , , PUNCT iajs-2566 223 76 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 223 77 ) ) PUNCT iajs-2566 223 78 } } PUNCT iajs-2566 223 79 β†’ β†’ SYM iajs-2566 223 80 𝛼 𝛼 X iajs-2566 223 81 π‘Žπ‘  π‘Žπ‘  ADP iajs-2566 223 82 π‘š π‘š NOUN iajs-2566 223 83 β†’ β†’ SYM iajs-2566 223 84 ∞ ∞ PROPN iajs-2566 223 85 and and CCONJ iajs-2566 223 86 { { PUNCT iajs-2566 223 87 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 223 88 , , PUNCT iajs-2566 223 89 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 223 90 , , PUNCT iajs-2566 223 91 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 223 92 ) ) PUNCT iajs-2566 223 93 } } PUNCT iajs-2566 223 94 is be AUX iajs-2566 223 95 a a DET iajs-2566 223 96 cauchy cauchy ADJ iajs-2566 223 97 sequence sequence NOUN iajs-2566 223 98 as as ADP iajs-2566 223 99 𝑛 𝑛 PROPN iajs-2566 223 100 , , PUNCT iajs-2566 223 101 π‘š π‘š PROPN iajs-2566 223 102 , , PUNCT iajs-2566 223 103 𝑙 𝑙 X iajs-2566 223 104 β†’ β†’ SYM iajs-2566 223 105 ∞ ∞ PROPN iajs-2566 223 106 , , PUNCT iajs-2566 223 107 then then ADV iajs-2566 223 108 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 223 109 , , PUNCT iajs-2566 223 110 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 223 111 , , PUNCT iajs-2566 223 112 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 223 113 ) ) PUNCT iajs-2566 223 114 β†’ β†’ SYM iajs-2566 223 115 𝛼 𝛼 X iajs-2566 223 116 as as ADP iajs-2566 223 117 𝑛 𝑛 PROPN iajs-2566 223 118 , , PUNCT iajs-2566 223 119 π‘š π‘š PROPN iajs-2566 223 120 , , PUNCT iajs-2566 223 121 𝑙 𝑙 DET iajs-2566 223 122 ⟢ ⟢ NOUN iajs-2566 223 123 ∞ ∞ NUM iajs-2566 223 124 where where SCONJ iajs-2566 223 125 𝐷𝑔define 𝐷𝑔define PROPN iajs-2566 223 126 in in ADP iajs-2566 223 127 corollary corollary ADJ iajs-2566 223 128 13 13 NUM iajs-2566 223 129 . . PUNCT iajs-2566 224 1 proof proof NOUN iajs-2566 224 2 since since SCONJ iajs-2566 224 3 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 224 4 , , PUNCT iajs-2566 224 5 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 224 6 , , PUNCT iajs-2566 224 7 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 224 8 ) ) PUNCT iajs-2566 224 9 β†’ β†’ SYM iajs-2566 224 10 𝛼 𝛼 X iajs-2566 224 11 π‘Žπ‘  π‘Žπ‘  ADP iajs-2566 224 12 π‘š π‘š PROPN iajs-2566 224 13 ⟢ ⟢ NOUN iajs-2566 224 14 ∞ ∞ PROPN iajs-2566 224 15 , , PUNCT iajs-2566 224 16 then then ADV iajs-2566 224 17 from from ADP iajs-2566 224 18 everyπœ– everyπœ– PROPN iajs-2566 224 19 > > X iajs-2566 224 20 0 0 PUNCT iajs-2566 225 1 there there PRON iajs-2566 225 2 exists exist VERB iajs-2566 225 3 𝑛0 𝑛0 VERB iajs-2566 225 4 ∈ ∈ NOUN iajs-2566 225 5 𝑁 𝑁 PROPN iajs-2566 225 6 such such ADJ iajs-2566 225 7 that that SCONJ iajs-2566 225 8 55 55 NUM iajs-2566 225 9 ibn ibn PROPN iajs-2566 225 10 al al PROPN iajs-2566 225 11 - - PUNCT iajs-2566 225 12 haitham haitham PROPN iajs-2566 225 13 jour jour X iajs-2566 225 14 . . PROPN iajs-2566 226 1 for for ADP iajs-2566 226 2 pure pure ADJ iajs-2566 226 3 & & CCONJ iajs-2566 226 4 appl appl PROPN iajs-2566 226 5 . . PUNCT iajs-2566 227 1 sci sci PROPN iajs-2566 227 2 . . PROPN iajs-2566 228 1 34 34 NUM iajs-2566 228 2 ( ( PUNCT iajs-2566 228 3 1 1 NUM iajs-2566 228 4 ) ) PUNCT iajs-2566 228 5 2021 2021 NUM iajs-2566 228 6 |𝐷𝑝(π›Όπ‘š |𝐷𝑝(π›Όπ‘š PROPN iajs-2566 228 7 , , PUNCT iajs-2566 228 8 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 228 9 , , PUNCT iajs-2566 228 10 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 228 11 ) ) PUNCT iajs-2566 228 12 βˆ’ βˆ’ PROPN iajs-2566 229 1 𝛼| 𝛼| NOUN iajs-2566 229 2 < < X iajs-2566 229 3 πœ– πœ– X iajs-2566 229 4 2 2 NUM iajs-2566 229 5 βˆ€ βˆ€ NOUN iajs-2566 229 6 π‘š π‘š X iajs-2566 229 7 > > X iajs-2566 229 8 𝑛0 𝑛0 PROPN iajs-2566 229 9 , , PUNCT iajs-2566 229 10 and and CCONJ iajs-2566 229 11 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 229 12 , , PUNCT iajs-2566 229 13 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 14 , , PUNCT iajs-2566 229 15 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 229 16 ) ) PUNCT iajs-2566 229 17 < < X iajs-2566 229 18 πœ€ πœ€ X iajs-2566 229 19 2 2 NUM iajs-2566 229 20 βˆ€ βˆ€ NOUN iajs-2566 229 21 𝑛 𝑛 PROPN iajs-2566 229 22 , , PUNCT iajs-2566 229 23 π‘š π‘š PROPN iajs-2566 229 24 , , PUNCT iajs-2566 229 25 𝑙 𝑙 PROPN iajs-2566 229 26 > > X iajs-2566 229 27 𝑛0 𝑛0 VERB iajs-2566 229 28 πœ– πœ– PROPN iajs-2566 229 29 2 2 NUM iajs-2566 229 30 > > X iajs-2566 229 31 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 PROPN iajs-2566 229 32 , , PUNCT iajs-2566 229 33 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 34 , , PUNCT iajs-2566 229 35 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 229 36 ) ) PUNCT iajs-2566 229 37 = = SYM iajs-2566 229 38 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 229 39 , , PUNCT iajs-2566 229 40 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 41 , , PUNCT iajs-2566 229 42 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 229 43 ) ) PUNCT iajs-2566 229 44 + + CCONJ iajs-2566 229 45 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 229 46 , , PUNCT iajs-2566 229 47 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 229 48 , , PUNCT iajs-2566 229 49 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 50 ) ) PUNCT iajs-2566 229 51 + + CCONJ iajs-2566 229 52 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 229 53 , , PUNCT iajs-2566 229 54 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 229 55 , , PUNCT iajs-2566 229 56 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 229 57 ) ) PUNCT iajs-2566 229 58 + + CCONJ iajs-2566 229 59 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 229 60 , , PUNCT iajs-2566 229 61 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 62 , , PUNCT iajs-2566 229 63 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 229 64 ) ) PUNCT iajs-2566 229 65 + + CCONJ iajs-2566 229 66 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 229 67 , , PUNCT iajs-2566 229 68 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 229 69 , , PUNCT iajs-2566 229 70 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 229 71 ) ) PUNCT iajs-2566 230 1 + + CCONJ iajs-2566 230 2 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 230 3 , , PUNCT iajs-2566 230 4 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 230 5 , , PUNCT iajs-2566 230 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 230 7 ) ) PUNCT iajs-2566 231 1 + + CCONJ iajs-2566 231 2 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 231 3 , , PUNCT iajs-2566 231 4 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 231 5 , , PUNCT iajs-2566 231 6 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 231 7 ) ) PUNCT iajs-2566 231 8 – – PUNCT iajs-2566 231 9 2𝐷𝑝(𝛼𝑛 2𝐷𝑝(𝛼𝑛 NUM iajs-2566 231 10 , , PUNCT iajs-2566 231 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 231 12 , , PUNCT iajs-2566 231 13 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 231 14 ) ) PUNCT iajs-2566 231 15 – – PUNCT iajs-2566 231 16 2𝐷𝑝(π›Όπ‘š 2𝐷𝑝(π›Όπ‘š NUM iajs-2566 231 17 , , PUNCT iajs-2566 231 18 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 231 19 , , PUNCT iajs-2566 231 20 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 231 21 ) ) PUNCT iajs-2566 231 22 – – PUNCT iajs-2566 231 23 3𝐷𝑝(𝛼𝑙 3𝐷𝑝(𝛼𝑙 NUM iajs-2566 231 24 , , PUNCT iajs-2566 231 25 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 231 26 , , PUNCT iajs-2566 231 27 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 231 28 ) ) PUNCT iajs-2566 231 29 . . PUNCT iajs-2566 232 1 β‡’ β‡’ PROPN iajs-2566 232 2 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 232 3 , , PUNCT iajs-2566 232 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 232 5 , , PUNCT iajs-2566 232 6 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 232 7 ) ) PUNCT iajs-2566 232 8 – – PUNCT iajs-2566 232 9 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 232 10 , , PUNCT iajs-2566 232 11 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 232 12 , , PUNCT iajs-2566 232 13 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 232 14 ) ) PUNCT iajs-2566 232 15 < < X iajs-2566 232 16 πœ– πœ– PROPN iajs-2566 232 17 2 2 NUM iajs-2566 232 18 so so SCONJ iajs-2566 232 19 that that SCONJ iajs-2566 232 20 |𝐷𝑝(𝛼n |𝐷𝑝(𝛼n PROPN iajs-2566 232 21 , , PUNCT iajs-2566 232 22 𝛼m 𝛼m PROPN iajs-2566 232 23 , , PUNCT iajs-2566 232 24 𝛼l 𝛼l NOUN iajs-2566 232 25 ) ) PUNCT iajs-2566 232 26 βˆ’ βˆ’ NOUN iajs-2566 232 27 𝛼|=|𝐷𝑝(𝛼𝑛 𝛼|=|𝐷𝑝(𝛼𝑛 NOUN iajs-2566 232 28 , , PUNCT iajs-2566 232 29 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 232 30 , , PUNCT iajs-2566 232 31 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 232 32 ) ) PUNCT iajs-2566 233 1 βˆ’ βˆ’ PROPN iajs-2566 233 2 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 233 3 , , PUNCT iajs-2566 233 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 233 5 , , PUNCT iajs-2566 233 6 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 233 7 ) ) PUNCT iajs-2566 233 8 + + CCONJ iajs-2566 233 9 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 233 10 , , PUNCT iajs-2566 233 11 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 233 12 , , PUNCT iajs-2566 233 13 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 233 14 ) ) PUNCT iajs-2566 233 15 βˆ’ βˆ’ PROPN iajs-2566 233 16 𝛼| 𝛼| NOUN iajs-2566 233 17 ≀ ≀ NOUN iajs-2566 233 18 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 NUM iajs-2566 233 19 , , PUNCT iajs-2566 233 20 π›Όπ‘š π›Όπ‘š AUX iajs-2566 233 21 , , PUNCT iajs-2566 233 22 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 233 23 ) ) PUNCT iajs-2566 233 24 βˆ’ βˆ’ PROPN iajs-2566 233 25 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 233 26 , , PUNCT iajs-2566 233 27 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 233 28 , , PUNCT iajs-2566 233 29 π›Όπ‘š)| π›Όπ‘š)| PROPN iajs-2566 233 30 + + SYM iajs-2566 233 31 |𝐷𝑝(π›Όπ‘š |𝐷𝑝(π›Όπ‘š ADJ iajs-2566 233 32 , , PUNCT iajs-2566 233 33 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 233 34 , , PUNCT iajs-2566 233 35 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 233 36 ) ) PUNCT iajs-2566 233 37 βˆ’ βˆ’ PROPN iajs-2566 233 38 𝛼| 𝛼| NOUN iajs-2566 233 39 < < X iajs-2566 233 40 πœ– πœ– X iajs-2566 233 41 2 2 NUM iajs-2566 233 42 + + CCONJ iajs-2566 233 43 πœ– πœ– X iajs-2566 233 44 2 2 NUM iajs-2566 233 45 < < X iajs-2566 233 46 πœ– πœ– X iajs-2566 233 47 hence hence ADV iajs-2566 233 48 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 233 49 , , PUNCT iajs-2566 233 50 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 233 51 , , PUNCT iajs-2566 233 52 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 233 53 ) ) PUNCT iajs-2566 233 54 β†’ β†’ SYM iajs-2566 233 55 𝛼 𝛼 X iajs-2566 233 56 π‘Žπ‘  π‘Žπ‘  PROPN iajs-2566 233 57 𝑛 𝑛 PROPN iajs-2566 233 58 , , PUNCT iajs-2566 233 59 π‘š π‘š PROPN iajs-2566 233 60 , , PUNCT iajs-2566 233 61 𝑙 𝑙 PRON iajs-2566 233 62 ⟢ ⟢ NOUN iajs-2566 233 63 ∞ ∞ NUM iajs-2566 233 64 βŽ• βŽ• NOUN iajs-2566 233 65 theorem theorem VERB iajs-2566 233 66 16 16 NUM iajs-2566 233 67 let let VERB iajs-2566 233 68 ( ( PUNCT iajs-2566 233 69 π‘Œ π‘Œ PROPN iajs-2566 233 70 , , PUNCT iajs-2566 233 71 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 233 72 ) ) PUNCT iajs-2566 233 73 be be VERB iajs-2566 233 74 a a DET iajs-2566 233 75 general general ADJ iajs-2566 233 76 partial partial ADJ iajs-2566 233 77 metric metric ADJ iajs-2566 233 78 space space NOUN iajs-2566 233 79 , , PUNCT iajs-2566 233 80 then then ADV iajs-2566 233 81 𝑖 𝑖 X iajs-2566 233 82 ) ) PUNCT iajs-2566 233 83 a a DET iajs-2566 233 84 sequence sequence NOUN iajs-2566 233 85 { { PUNCT iajs-2566 233 86 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 233 87 } } PUNCT iajs-2566 233 88 is be AUX iajs-2566 233 89 a a DET iajs-2566 233 90 cauchy cauchy ADJ iajs-2566 233 91 sequence sequence NOUN iajs-2566 233 92 in in ADP iajs-2566 233 93 a a DET iajs-2566 233 94 general general ADJ iajs-2566 233 95 partial partial ADJ iajs-2566 233 96 metric metric ADJ iajs-2566 233 97 space space NOUN iajs-2566 233 98 ( ( PUNCT iajs-2566 233 99 π‘Œ π‘Œ PROPN iajs-2566 233 100 , , PUNCT iajs-2566 233 101 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 233 102 ) ) PUNCT iajs-2566 234 1 if if SCONJ iajs-2566 234 2 and and CCONJ iajs-2566 234 3 only only ADV iajs-2566 234 4 if if SCONJ iajs-2566 234 5 { { PUNCT iajs-2566 234 6 𝛼𝑛 𝛼𝑛 X iajs-2566 234 7 } } PUNCT iajs-2566 234 8 is be AUX iajs-2566 234 9 a a DET iajs-2566 234 10 cauchy cauchy ADJ iajs-2566 234 11 sequence sequence NOUN iajs-2566 234 12 in in ADP iajs-2566 234 13 ( ( PUNCT iajs-2566 234 14 π‘Œ π‘Œ PROPN iajs-2566 234 15 , , PUNCT iajs-2566 234 16 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 234 17 ) ) PUNCT iajs-2566 234 18 . . PUNCT iajs-2566 235 1 𝑖𝑖 𝑖𝑖 X iajs-2566 235 2 ) ) PUNCT iajs-2566 235 3 a a DET iajs-2566 235 4 general general ADJ iajs-2566 235 5 partial partial ADJ iajs-2566 235 6 metric metric ADJ iajs-2566 235 7 space space NOUN iajs-2566 235 8 ( ( PUNCT iajs-2566 235 9 π‘Œ π‘Œ PROPN iajs-2566 235 10 , , PUNCT iajs-2566 235 11 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 235 12 ) ) PUNCT iajs-2566 235 13 is be AUX iajs-2566 235 14 complete complete ADJ iajs-2566 235 15 if if SCONJ iajs-2566 235 16 ( ( PUNCT iajs-2566 235 17 π‘Œ π‘Œ PROPN iajs-2566 235 18 , , PUNCT iajs-2566 235 19 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 235 20 ) ) PUNCT iajs-2566 235 21 is be AUX iajs-2566 235 22 complete complete ADJ iajs-2566 235 23 . . PUNCT iajs-2566 236 1 where where SCONJ iajs-2566 236 2 𝐷𝑔define 𝐷𝑔define PROPN iajs-2566 236 3 in in ADP iajs-2566 236 4 corollary corollary ADJ iajs-2566 236 5 13 13 NUM iajs-2566 236 6 proof proof NOUN iajs-2566 236 7 π’Š π’Š X iajs-2566 236 8 first first ADV iajs-2566 236 9 , , PUNCT iajs-2566 236 10 we we PRON iajs-2566 236 11 must must AUX iajs-2566 236 12 prove prove VERB iajs-2566 236 13 that that SCONJ iajs-2566 236 14 each each DET iajs-2566 236 15 cauchy cauchy ADJ iajs-2566 236 16 sequence sequence NOUN iajs-2566 236 17 in in ADP iajs-2566 236 18 ( ( PUNCT iajs-2566 236 19 π‘Œ π‘Œ PROPN iajs-2566 236 20 , , PUNCT iajs-2566 236 21 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 236 22 ) ) PUNCT iajs-2566 236 23 is be AUX iajs-2566 236 24 cauchy cauchy ADJ iajs-2566 236 25 in in ADP iajs-2566 236 26 ( ( PUNCT iajs-2566 236 27 π‘Œ π‘Œ PROPN iajs-2566 236 28 , , PUNCT iajs-2566 236 29 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 236 30 ) ) PUNCT iajs-2566 236 31 . . PUNCT iajs-2566 237 1 then then ADV iajs-2566 237 2 , , PUNCT iajs-2566 237 3 there there PRON iajs-2566 237 4 exists exist VERB iajs-2566 237 5 𝛼 𝛼 PROPN iajs-2566 237 6 ∈ ∈ PROPN iajs-2566 237 7 𝑅 𝑅 PROPN iajs-2566 237 8 such such ADJ iajs-2566 237 9 that that PRON iajs-2566 237 10 , , PUNCT iajs-2566 237 11 βˆ€πœ– βˆ€πœ– NOUN iajs-2566 237 12 > > X iajs-2566 237 13 0 0 PUNCT iajs-2566 237 14 there there PRON iajs-2566 237 15 is be VERB iajs-2566 237 16 𝑛0 𝑛0 VERB iajs-2566 237 17 ∈ ∈ NOUN iajs-2566 237 18 𝑁 𝑁 NOUN iajs-2566 237 19 with with ADP iajs-2566 237 20 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 NOUN iajs-2566 237 21 , , PUNCT iajs-2566 237 22 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 237 23 , , PUNCT iajs-2566 237 24 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 237 25 ) ) PUNCT iajs-2566 237 26 βˆ’ βˆ’ PROPN iajs-2566 238 1 𝛼| 𝛼| NOUN iajs-2566 238 2 < < X iajs-2566 238 3 πœ– πœ– PROPN iajs-2566 238 4 14 14 NUM iajs-2566 238 5 βˆ€ βˆ€ NOUN iajs-2566 238 6 n n CCONJ iajs-2566 238 7 , , PUNCT iajs-2566 238 8 m m PROPN iajs-2566 238 9 , , PUNCT iajs-2566 238 10 l l PROPN iajs-2566 238 11 β‰₯ β‰₯ PROPN iajs-2566 238 12 n0 n0 NUM iajs-2566 238 13 . . PUNCT iajs-2566 239 1 hence hence ADV iajs-2566 239 2 , , PUNCT iajs-2566 239 3 |dg(𝛼n |dg(𝛼n PROPN iajs-2566 239 4 , , PUNCT iajs-2566 239 5 𝛼m 𝛼m PROPN iajs-2566 239 6 , , PUNCT iajs-2566 239 7 𝛼l)|= 𝛼l)|= NUM iajs-2566 239 8 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 NOUN iajs-2566 239 9 , , PUNCT iajs-2566 239 10 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 239 11 , , PUNCT iajs-2566 239 12 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 239 13 ) ) PUNCT iajs-2566 239 14 + + CCONJ iajs-2566 239 15 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 239 16 , , PUNCT iajs-2566 239 17 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 239 18 , , PUNCT iajs-2566 239 19 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 239 20 ) ) PUNCT iajs-2566 239 21 + + CCONJ iajs-2566 239 22 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 239 23 , , PUNCT iajs-2566 239 24 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 239 25 , , PUNCT iajs-2566 239 26 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 239 27 ) ) PUNCT iajs-2566 239 28 + + CCONJ iajs-2566 239 29 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 239 30 , , PUNCT iajs-2566 239 31 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 239 32 , , PUNCT iajs-2566 239 33 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 239 34 ) ) PUNCT iajs-2566 239 35 + + CCONJ iajs-2566 239 36 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 239 37 , , PUNCT iajs-2566 239 38 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 239 39 , , PUNCT iajs-2566 239 40 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 239 41 ) ) PUNCT iajs-2566 240 1 + + CCONJ iajs-2566 240 2 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 VERB iajs-2566 240 3 , , PUNCT iajs-2566 240 4 𝛼𝑙 𝛼𝑙 INTJ iajs-2566 240 5 , , PUNCT iajs-2566 240 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 240 7 ) ) PUNCT iajs-2566 240 8 + + NUM iajs-2566 240 9 𝐷 𝐷 NOUN iajs-2566 240 10 𝑝(𝛼𝑙 𝑝(𝛼𝑙 NOUN iajs-2566 240 11 , , PUNCT iajs-2566 240 12 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 240 13 , , PUNCT iajs-2566 240 14 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 240 15 ) ) PUNCT iajs-2566 240 16 βˆ’ βˆ’ PROPN iajs-2566 240 17 2𝐷𝑝(𝛼𝑛 2𝐷𝑝(𝛼𝑛 NUM iajs-2566 240 18 , , PUNCT iajs-2566 240 19 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 240 20 , , PUNCT iajs-2566 240 21 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 240 22 ) ) PUNCT iajs-2566 240 23 βˆ’ βˆ’ PROPN iajs-2566 240 24 2𝐷𝑝(π›Όπ‘š 2𝐷𝑝(π›Όπ‘š NUM iajs-2566 240 25 , , PUNCT iajs-2566 240 26 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 240 27 , , PUNCT iajs-2566 240 28 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 240 29 ) ) PUNCT iajs-2566 240 30 βˆ’ βˆ’ PROPN iajs-2566 241 1 3𝐷𝑝(𝛼𝑙 3𝐷𝑝(𝛼𝑙 NUM iajs-2566 241 2 , , PUNCT iajs-2566 241 3 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 241 4 , , PUNCT iajs-2566 241 5 𝛼𝑙)| 𝛼𝑙)| PROPN iajs-2566 241 6 ≀ ≀ NOUN iajs-2566 241 7 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 NUM iajs-2566 241 8 , , PUNCT iajs-2566 241 9 π›Όπ‘š π›Όπ‘š AUX iajs-2566 241 10 , , PUNCT iajs-2566 241 11 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 241 12 ) ) PUNCT iajs-2566 241 13 βˆ’ βˆ’ PROPN iajs-2566 242 1 𝛼| 𝛼| NOUN iajs-2566 242 2 + + SYM iajs-2566 242 3 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 PROPN iajs-2566 242 4 , , PUNCT iajs-2566 242 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 242 6 , , PUNCT iajs-2566 242 7 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 242 8 ) ) PUNCT iajs-2566 242 9 βˆ’ βˆ’ PROPN iajs-2566 242 10 𝛼| 𝛼| NOUN iajs-2566 242 11 + + SYM iajs-2566 242 12 |𝐷𝑝(𝛼𝑛 |𝐷𝑝(𝛼𝑛 PROPN iajs-2566 242 13 , , PUNCT iajs-2566 242 14 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 242 15 , , PUNCT iajs-2566 242 16 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 242 17 ) ) PUNCT iajs-2566 242 18 βˆ’ βˆ’ PROPN iajs-2566 242 19 𝛼| 𝛼| NOUN iajs-2566 242 20 + + SYM iajs-2566 242 21 |𝐷 |𝐷 NOUN iajs-2566 242 22 𝑝(π›Όπ‘š 𝑝(π›Όπ‘š PROPN iajs-2566 242 23 , , PUNCT iajs-2566 242 24 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 242 25 , , PUNCT iajs-2566 242 26 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 242 27 ) ) PUNCT iajs-2566 242 28 βˆ’ βˆ’ PROPN iajs-2566 243 1 𝛼| 𝛼| PROPN iajs-2566 243 2 + + SYM iajs-2566 243 3 |𝐷𝑝(π›Όπ‘š |𝐷𝑝(π›Όπ‘š CCONJ iajs-2566 243 4 , , PUNCT iajs-2566 243 5 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 243 6 , , PUNCT iajs-2566 243 7 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 243 8 ) ) PUNCT iajs-2566 243 9 βˆ’ βˆ’ PROPN iajs-2566 243 10 𝛼| 𝛼| PROPN iajs-2566 243 11 + + NUM iajs-2566 243 12 |𝐷𝑝(𝛼𝑙 |𝐷𝑝(𝛼𝑙 PROPN iajs-2566 243 13 , , PUNCT iajs-2566 243 14 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 243 15 , , PUNCT iajs-2566 243 16 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 243 17 ) ) PUNCT iajs-2566 243 18 βˆ’ βˆ’ PROPN iajs-2566 243 19 𝛼| 𝛼| PROPN iajs-2566 243 20 + + NUM iajs-2566 243 21 |𝐷𝑝(𝛼𝑙 |𝐷𝑝(𝛼𝑙 PROPN iajs-2566 243 22 , , PUNCT iajs-2566 243 23 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 243 24 , , PUNCT iajs-2566 243 25 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 243 26 ) ) PUNCT iajs-2566 243 27 βˆ’ βˆ’ PROPN iajs-2566 243 28 𝛼|-2|𝐷𝑝(𝛼𝑛 𝛼|-2|𝐷𝑝(𝛼𝑛 NOUN iajs-2566 243 29 , , PUNCT iajs-2566 243 30 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 243 31 , , PUNCT iajs-2566 243 32 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 243 33 ) ) PUNCT iajs-2566 243 34 βˆ’ βˆ’ PROPN iajs-2566 243 35 𝛼 𝛼 INTJ iajs-2566 243 36 | | ADV iajs-2566 243 37 βˆ’ βˆ’ PROPN iajs-2566 243 38 2|𝐷𝑝(π›Όπ‘š 2|𝐷𝑝(π›Όπ‘š NUM iajs-2566 243 39 , , PUNCT iajs-2566 243 40 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 243 41 , , PUNCT iajs-2566 243 42 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 243 43 ) ) PUNCT iajs-2566 243 44 βˆ’ βˆ’ PROPN iajs-2566 243 45 𝛼| 𝛼| NOUN iajs-2566 243 46 βˆ’ βˆ’ NOUN iajs-2566 243 47 3|𝐷𝑝(𝛼𝑙 3|𝐷𝑝(𝛼𝑙 NUM iajs-2566 243 48 , , PUNCT iajs-2566 243 49 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 243 50 , , PUNCT iajs-2566 243 51 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 243 52 ) ) PUNCT iajs-2566 243 53 βˆ’ βˆ’ PROPN iajs-2566 243 54 𝛼| 𝛼| NOUN iajs-2566 243 55 Ξ΅ Ξ΅ PROPN iajs-2566 243 56 14 14 NUM iajs-2566 243 57 < < X iajs-2566 243 58 νœ€ νœ€ X iajs-2566 243 59 βˆ€ βˆ€ X iajs-2566 243 60 n n CCONJ iajs-2566 243 61 , , PUNCT iajs-2566 243 62 m m PROPN iajs-2566 243 63 , , PUNCT iajs-2566 243 64 l l PROPN iajs-2566 243 65 β‰₯ β‰₯ PROPN iajs-2566 243 66 n0 n0 NUM iajs-2566 243 67 . . PUNCT iajs-2566 244 1 hence hence ADV iajs-2566 244 2 , , PUNCT iajs-2566 244 3 { { PUNCT iajs-2566 244 4 𝛼𝑛 𝛼𝑛 ADP iajs-2566 244 5 } } PUNCT iajs-2566 244 6 is be AUX iajs-2566 244 7 a a DET iajs-2566 244 8 cauchy cauchy ADJ iajs-2566 244 9 sequence sequence NOUN iajs-2566 244 10 in(π‘Œ in(π‘Œ PROPN iajs-2566 244 11 , , PUNCT iajs-2566 244 12 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 244 13 ) ) PUNCT iajs-2566 244 14 . . PUNCT iajs-2566 245 1 conversely conversely ADV iajs-2566 245 2 , , PUNCT iajs-2566 245 3 now now ADV iajs-2566 245 4 we we PRON iajs-2566 245 5 must must AUX iajs-2566 245 6 prove prove VERB iajs-2566 245 7 { { PUNCT iajs-2566 245 8 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 9 } } PUNCT iajs-2566 245 10 is be AUX iajs-2566 245 11 cauchy cauchy ADJ iajs-2566 245 12 sequence sequence NOUN iajs-2566 245 13 in in ADP iajs-2566 245 14 ( ( PUNCT iajs-2566 245 15 π‘Œ π‘Œ PROPN iajs-2566 245 16 , , PUNCT iajs-2566 245 17 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 245 18 ) ) PUNCT iajs-2566 245 19 since since SCONJ iajs-2566 245 20 { { PUNCT iajs-2566 245 21 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 22 } } PUNCT iajs-2566 245 23 is be AUX iajs-2566 245 24 a a DET iajs-2566 245 25 cauchy cauchy ADJ iajs-2566 245 26 sequence sequence NOUN iajs-2566 245 27 in in ADP iajs-2566 245 28 ( ( PUNCT iajs-2566 245 29 π‘Œ π‘Œ PROPN iajs-2566 245 30 , , PUNCT iajs-2566 245 31 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 245 32 ) ) PUNCT iajs-2566 245 33 π‘ π‘œ π‘ π‘œ ADP iajs-2566 245 34 βˆ€πœ– βˆ€πœ– PROPN iajs-2566 245 35 > > X iajs-2566 245 36 0 0 NUM iajs-2566 245 37 , , PUNCT iajs-2566 245 38 βˆƒ βˆƒ PROPN iajs-2566 245 39 𝑛0 𝑛0 VERB iajs-2566 245 40 ∈ ∈ NOUN iajs-2566 245 41 𝑁 𝑁 PROPN iajs-2566 245 42 such such ADJ iajs-2566 245 43 that that DET iajs-2566 245 44 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 245 45 , , PUNCT iajs-2566 245 46 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 47 , , PUNCT iajs-2566 245 48 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 49 ) ) PUNCT iajs-2566 245 50 < < X iajs-2566 245 51 πœ– πœ– PROPN iajs-2566 245 52 2 2 NUM iajs-2566 245 53 βˆ€π‘› βˆ€π‘› NOUN iajs-2566 245 54 , , PUNCT iajs-2566 245 55 π‘š π‘š PROPN iajs-2566 245 56 , , PUNCT iajs-2566 245 57 𝑙 𝑙 PROPN iajs-2566 245 58 > > X iajs-2566 245 59 𝑛0 𝑛0 VERB iajs-2566 245 60 πœ– πœ– PROPN iajs-2566 245 61 2 2 NUM iajs-2566 245 62 > > PUNCT iajs-2566 245 63 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 PROPN iajs-2566 245 64 , , PUNCT iajs-2566 245 65 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 66 , , PUNCT iajs-2566 245 67 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 68 ) ) PUNCT iajs-2566 245 69 = = SYM iajs-2566 245 70 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 245 71 , , PUNCT iajs-2566 245 72 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 73 , , PUNCT iajs-2566 245 74 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 75 ) ) PUNCT iajs-2566 245 76 + + CCONJ iajs-2566 245 77 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 245 78 , , PUNCT iajs-2566 245 79 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 80 , , PUNCT iajs-2566 245 81 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 82 ) ) PUNCT iajs-2566 245 83 + + CCONJ iajs-2566 245 84 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 245 85 , , PUNCT iajs-2566 245 86 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 87 , , PUNCT iajs-2566 245 88 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 89 ) ) PUNCT iajs-2566 245 90 + + CCONJ iajs-2566 245 91 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 245 92 , , PUNCT iajs-2566 245 93 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 94 , , PUNCT iajs-2566 245 95 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 96 ) ) PUNCT iajs-2566 245 97 + + CCONJ iajs-2566 245 98 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 245 99 , , PUNCT iajs-2566 245 100 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 101 , , PUNCT iajs-2566 245 102 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 103 ) ) PUNCT iajs-2566 245 104 + + CCONJ iajs-2566 245 105 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 245 106 , , PUNCT iajs-2566 245 107 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 108 , , PUNCT iajs-2566 245 109 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 110 ) ) PUNCT iajs-2566 245 111 + + CCONJ iajs-2566 245 112 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 245 113 , , PUNCT iajs-2566 245 114 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 115 , , PUNCT iajs-2566 245 116 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 117 ) ) PUNCT iajs-2566 245 118 – – PUNCT iajs-2566 245 119 2𝐷𝑝(𝛼𝑛 2𝐷𝑝(𝛼𝑛 NUM iajs-2566 245 120 , , PUNCT iajs-2566 245 121 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 122 , , PUNCT iajs-2566 245 123 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 245 124 ) ) PUNCT iajs-2566 245 125 – – PUNCT iajs-2566 245 126 2𝐷𝑝(π›Όπ‘š 2𝐷𝑝(π›Όπ‘š NUM iajs-2566 245 127 , , PUNCT iajs-2566 245 128 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 129 , , PUNCT iajs-2566 245 130 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 245 131 ) ) PUNCT iajs-2566 245 132 – – PUNCT iajs-2566 245 133 3𝐷𝑝(𝛼𝑙 3𝐷𝑝(𝛼𝑙 NUM iajs-2566 245 134 , , PUNCT iajs-2566 245 135 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 136 , , PUNCT iajs-2566 245 137 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 245 138 ) ) PUNCT iajs-2566 245 139 56 56 NUM iajs-2566 245 140 ibn ibn PROPN iajs-2566 245 141 al al PROPN iajs-2566 245 142 - - PUNCT iajs-2566 245 143 haitham haitham PROPN iajs-2566 245 144 jour jour X iajs-2566 245 145 . . PROPN iajs-2566 245 146 for for ADP iajs-2566 245 147 pure pure ADJ iajs-2566 245 148 & & CCONJ iajs-2566 245 149 appl appl PROPN iajs-2566 245 150 . . PUNCT iajs-2566 246 1 sci sci PROPN iajs-2566 246 2 . . PROPN iajs-2566 247 1 34 34 NUM iajs-2566 247 2 ( ( PUNCT iajs-2566 247 3 1 1 NUM iajs-2566 247 4 ) ) PUNCT iajs-2566 247 5 2021 2021 NUM iajs-2566 247 6 β‡’ β‡’ NOUN iajs-2566 247 7 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 8 , , PUNCT iajs-2566 247 9 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 10 , , PUNCT iajs-2566 247 11 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 12 ) ) PUNCT iajs-2566 247 13 – – PUNCT iajs-2566 247 14 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 15 , , PUNCT iajs-2566 247 16 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 17 , , PUNCT iajs-2566 247 18 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 19 ) ) PUNCT iajs-2566 247 20 ≀ ≀ NOUN iajs-2566 247 21 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 PROPN iajs-2566 247 22 , , PUNCT iajs-2566 247 23 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 24 , , PUNCT iajs-2566 247 25 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 26 ) ) PUNCT iajs-2566 247 27 < < X iajs-2566 247 28 πœ– πœ– PROPN iajs-2566 247 29 2 2 NUM iajs-2566 247 30 by by ADP iajs-2566 247 31 compensation compensation NOUN iajs-2566 247 32 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 PROPN iajs-2566 247 33 , , PUNCT iajs-2566 247 34 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 35 , , PUNCT iajs-2566 247 36 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 37 ) ) PUNCT iajs-2566 247 38 to to ADP iajs-2566 247 39 two two NUM iajs-2566 247 40 parties party NOUN iajs-2566 247 41 , , PUNCT iajs-2566 247 42 we we PRON iajs-2566 247 43 have have VERB iajs-2566 247 44 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 45 , , PUNCT iajs-2566 247 46 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 47 , , PUNCT iajs-2566 247 48 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 49 ) ) PUNCT iajs-2566 247 50 ≀ ≀ NOUN iajs-2566 247 51 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 247 52 , , PUNCT iajs-2566 247 53 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 54 , , PUNCT iajs-2566 247 55 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 56 ) ) PUNCT iajs-2566 247 57 + + CCONJ iajs-2566 247 58 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 59 , , PUNCT iajs-2566 247 60 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 61 , , PUNCT iajs-2566 247 62 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 63 ) ) PUNCT iajs-2566 247 64 < < X iajs-2566 247 65 πœ– πœ– PROPN iajs-2566 247 66 2 2 NUM iajs-2566 247 67 + + CCONJ iajs-2566 247 68 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 69 , , PUNCT iajs-2566 247 70 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 71 , , PUNCT iajs-2566 247 72 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 73 ) ) PUNCT iajs-2566 247 74 𝐴𝑛𝑑 𝐴𝑛𝑑 PROPN iajs-2566 247 75 𝑠𝑖𝑛𝑐𝑒 𝑠𝑖𝑛𝑐𝑒 PROPN iajs-2566 247 76 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 247 77 , , PUNCT iajs-2566 247 78 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 79 , , PUNCT iajs-2566 247 80 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 81 ) ) PUNCT iajs-2566 247 82 ≀ ≀ NUM iajs-2566 247 83 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 84 , , PUNCT iajs-2566 247 85 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 86 , , PUNCT iajs-2566 247 87 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 88 ) ) PUNCT iajs-2566 247 89 π‘ π‘œ π‘ π‘œ ADP iajs-2566 247 90 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 247 91 , , PUNCT iajs-2566 247 92 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 93 , , PUNCT iajs-2566 247 94 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 95 ) ) PUNCT iajs-2566 247 96 ≀ ≀ NUM iajs-2566 247 97 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 98 , , PUNCT iajs-2566 247 99 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 100 , , PUNCT iajs-2566 247 101 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 102 ) ) PUNCT iajs-2566 247 103 ≀ ≀ NOUN iajs-2566 247 104 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 247 105 , , PUNCT iajs-2566 247 106 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 107 , , PUNCT iajs-2566 247 108 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 247 109 ) ) PUNCT iajs-2566 247 110 + + CCONJ iajs-2566 247 111 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 112 , , PUNCT iajs-2566 247 113 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 114 , , PUNCT iajs-2566 247 115 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 116 ) ) PUNCT iajs-2566 247 117 < < X iajs-2566 247 118 πœ– πœ– PROPN iajs-2566 247 119 2 2 NUM iajs-2566 247 120 + + CCONJ iajs-2566 247 121 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 122 , , PUNCT iajs-2566 247 123 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 124 , , PUNCT iajs-2566 247 125 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 126 ) ) PUNCT iajs-2566 247 127 β‡’ β‡’ PROPN iajs-2566 247 128 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 247 129 , , PUNCT iajs-2566 247 130 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 131 , , PUNCT iajs-2566 247 132 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 133 ) ) PUNCT iajs-2566 247 134 ≀ ≀ NOUN iajs-2566 247 135 πœ– πœ– X iajs-2566 247 136 2 2 NUM iajs-2566 247 137 + + CCONJ iajs-2566 247 138 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 247 139 , , PUNCT iajs-2566 247 140 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 141 , , PUNCT iajs-2566 247 142 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 143 ) ) PUNCT iajs-2566 247 144 βˆ€ βˆ€ X iajs-2566 247 145 𝑛 𝑛 NOUN iajs-2566 247 146 , , PUNCT iajs-2566 247 147 π‘š π‘š X iajs-2566 247 148 > > X iajs-2566 247 149 𝑛0 𝑛0 VERB iajs-2566 247 150 𝐿𝑒𝑑 𝐿𝑒𝑑 PROPN iajs-2566 247 151 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 152 = = SYM iajs-2566 247 153 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 PROPN iajs-2566 247 154 , , PUNCT iajs-2566 247 155 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 156 , , PUNCT iajs-2566 247 157 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 158 ) ) PUNCT iajs-2566 247 159 ∈ ∈ PROPN iajs-2566 247 160 𝑅 𝑅 PROPN iajs-2566 247 161 π‘ π‘’π‘β„Ž π‘ π‘’π‘β„Ž NOUN iajs-2566 247 162 π‘‘β„Žπ‘Žπ‘‘ π‘‘β„Žπ‘Žπ‘‘ PROPN iajs-2566 247 163 | | ADV iajs-2566 247 164 𝛼 𝛼 VERB iajs-2566 247 165 π‘š π‘š NOUN iajs-2566 247 166 – – PUNCT iajs-2566 247 167 𝛼𝑛| 𝛼𝑛| ADJ iajs-2566 247 168 < < X iajs-2566 247 169 πœ– πœ– PROPN iajs-2566 247 170 2 2 NUM iajs-2566 247 171 ∴ ∴ PROPN iajs-2566 247 172 { { PUNCT iajs-2566 247 173 Ξ±π‘š Ξ±π‘š NOUN iajs-2566 247 174 } } PUNCT iajs-2566 247 175 is be AUX iajs-2566 247 176 a a DET iajs-2566 247 177 cauchy cauchy ADJ iajs-2566 247 178 sequence sequence NOUN iajs-2566 247 179 , , PUNCT iajs-2566 247 180 ∴ ∴ PROPN iajs-2566 247 181 { { PUNCT iajs-2566 247 182 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 247 183 } } PUNCT iajs-2566 247 184 β†’ β†’ SYM iajs-2566 247 185 𝛼 𝛼 X iajs-2566 247 186 , , PUNCT iajs-2566 247 187 ∴ ∴ PROPN iajs-2566 247 188 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 247 189 , , PUNCT iajs-2566 247 190 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 191 , , PUNCT iajs-2566 247 192 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 247 193 ) ) PUNCT iajs-2566 247 194 β†’ β†’ SYM iajs-2566 247 195 𝛼 𝛼 X iajs-2566 247 196 ∈ ∈ PROPN iajs-2566 247 197 𝑅 𝑅 PROPN iajs-2566 247 198 then then ADV iajs-2566 247 199 by by ADP iajs-2566 247 200 lemma lemma PROPN iajs-2566 247 201 15 15 NUM iajs-2566 247 202 , , PUNCT iajs-2566 247 203 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 247 204 , , PUNCT iajs-2566 247 205 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 206 , , PUNCT iajs-2566 247 207 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 247 208 ) ) PUNCT iajs-2566 247 209 is be AUX iajs-2566 247 210 cauchy cauchy ADJ iajs-2566 247 211 sequence sequence NOUN iajs-2566 247 212 in in ADP iajs-2566 247 213 ( ( PUNCT iajs-2566 247 214 π‘Œ π‘Œ PROPN iajs-2566 247 215 , , PUNCT iajs-2566 247 216 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 247 217 ) ) PUNCT iajs-2566 247 218 . . PUNCT iajs-2566 248 1 βŽ• βŽ• PROPN iajs-2566 249 1 ii ii NOUN iajs-2566 249 2 : : PUNCT iajs-2566 249 3 if if SCONJ iajs-2566 249 4 { { PUNCT iajs-2566 249 5 𝛼𝑛 𝛼𝑛 X iajs-2566 249 6 } } PUNCT iajs-2566 249 7 is be AUX iajs-2566 249 8 a a DET iajs-2566 249 9 cauchy cauchy ADJ iajs-2566 249 10 sequence sequence NOUN iajs-2566 249 11 in in ADP iajs-2566 249 12 ( ( PUNCT iajs-2566 249 13 π‘Œ π‘Œ PROPN iajs-2566 249 14 , , PUNCT iajs-2566 249 15 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 249 16 ) ) PUNCT iajs-2566 249 17 , , PUNCT iajs-2566 249 18 then then ADV iajs-2566 249 19 it it PRON iajs-2566 249 20 is be AUX iajs-2566 249 21 a a DET iajs-2566 249 22 cauchy cauchy ADJ iajs-2566 249 23 sequence sequence NOUN iajs-2566 249 24 in in ADP iajs-2566 249 25 ( ( PUNCT iajs-2566 249 26 π‘Œ π‘Œ PROPN iajs-2566 249 27 , , PUNCT iajs-2566 249 28 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 249 29 ) ) PUNCT iajs-2566 249 30 and and CCONJ iajs-2566 249 31 since since SCONJ iajs-2566 249 32 dmetric dmetric ADJ iajs-2566 249 33 ( ( PUNCT iajs-2566 249 34 π‘Œ π‘Œ PROPN iajs-2566 249 35 , , PUNCT iajs-2566 249 36 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 249 37 ) ) PUNCT iajs-2566 249 38 is be AUX iajs-2566 249 39 complete complete ADJ iajs-2566 249 40 then then ADV iajs-2566 249 41 there there PRON iajs-2566 249 42 exists exist VERB iajs-2566 249 43 𝛼 𝛼 PRON iajs-2566 249 44 ∈ ∈ PROPN iajs-2566 249 45 π‘Œ π‘Œ PROPN iajs-2566 249 46 such such ADJ iajs-2566 249 47 that that SCONJ iajs-2566 249 48 limn limn NOUN iajs-2566 249 49 , , PUNCT iajs-2566 249 50 m m VERB iajs-2566 249 51 β†’βˆž β†’βˆž PROPN iajs-2566 249 52 d𝑔(𝛼𝑛 d𝑔(𝛼𝑛 NOUN iajs-2566 249 53 , , PUNCT iajs-2566 249 54 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 249 55 , , PUNCT iajs-2566 249 56 𝛼 𝛼 NOUN iajs-2566 249 57 ) ) PUNCT iajs-2566 249 58 = = SYM iajs-2566 249 59 0 0 NUM iajs-2566 249 60 , , PUNCT iajs-2566 249 61 hence hence ADV iajs-2566 249 62 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 249 63 , , PUNCT iajs-2566 249 64 π‘šβ†’βˆž[𝐷𝑝(𝛼𝑛 π‘šβ†’βˆž[𝐷𝑝(𝛼𝑛 PROPN iajs-2566 249 65 , , PUNCT iajs-2566 249 66 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 249 67 , , PUNCT iajs-2566 249 68 𝛼 𝛼 NOUN iajs-2566 249 69 ) ) PUNCT iajs-2566 249 70 + + CCONJ iajs-2566 249 71 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 249 72 , , PUNCT iajs-2566 249 73 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 249 74 , , PUNCT iajs-2566 249 75 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 249 76 ) ) PUNCT iajs-2566 249 77 + + CCONJ iajs-2566 250 1 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 250 2 , , PUNCT iajs-2566 250 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 250 4 , , PUNCT iajs-2566 250 5 𝛼 𝛼 NOUN iajs-2566 250 6 ) ) PUNCT iajs-2566 250 7 + + CCONJ iajs-2566 250 8 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 250 9 , , PUNCT iajs-2566 250 10 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 250 11 , , PUNCT iajs-2566 250 12 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 250 13 ) ) PUNCT iajs-2566 250 14 + + CCONJ iajs-2566 250 15 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 250 16 , , PUNCT iajs-2566 250 17 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 250 18 , , PUNCT iajs-2566 250 19 𝛼 𝛼 NOUN iajs-2566 250 20 ) ) PUNCT iajs-2566 251 1 + + CCONJ iajs-2566 251 2 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 251 3 , , PUNCT iajs-2566 251 4 𝛼 𝛼 INTJ iajs-2566 251 5 , , PUNCT iajs-2566 251 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 251 7 ) ) PUNCT iajs-2566 251 8 + + CCONJ iajs-2566 251 9 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 251 10 , , PUNCT iajs-2566 251 11 𝛼 𝛼 PRON iajs-2566 251 12 , , PUNCT iajs-2566 251 13 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 251 14 ) ) PUNCT iajs-2566 251 15 – – PUNCT iajs-2566 251 16 2𝐷𝑝(𝛼𝑛 2𝐷𝑝(𝛼𝑛 NUM iajs-2566 251 17 , , PUNCT iajs-2566 251 18 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 251 19 , , PUNCT iajs-2566 251 20 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 251 21 ) ) PUNCT iajs-2566 251 22 – – PUNCT iajs-2566 251 23 2𝐷𝑝(π›Όπ‘š 2𝐷𝑝(π›Όπ‘š NUM iajs-2566 251 24 , , PUNCT iajs-2566 251 25 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 251 26 , , PUNCT iajs-2566 251 27 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 251 28 ) ) PUNCT iajs-2566 251 29 – – PUNCT iajs-2566 251 30 3𝐷𝑝(𝛼 3𝐷𝑝(𝛼 NUM iajs-2566 251 31 , , PUNCT iajs-2566 251 32 𝛼 𝛼 INTJ iajs-2566 251 33 , , PUNCT iajs-2566 251 34 𝛼 𝛼 NOUN iajs-2566 251 35 ) ) PUNCT iajs-2566 251 36 ] ] PUNCT iajs-2566 252 1 = = PUNCT iajs-2566 252 2 0 0 PUNCT iajs-2566 252 3 there there ADV iajs-2566 252 4 for for ADP iajs-2566 252 5 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 252 6 π‘š π‘š PROPN iajs-2566 252 7 β†’βˆž[𝐷𝑝(𝛼𝑛 β†’βˆž[𝐷𝑝(𝛼𝑛 PROPN iajs-2566 252 8 , , PUNCT iajs-2566 252 9 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 252 10 , , PUNCT iajs-2566 252 11 𝛼 𝛼 NOUN iajs-2566 252 12 ) ) PUNCT iajs-2566 252 13 – – PUNCT iajs-2566 252 14 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 252 15 , , PUNCT iajs-2566 252 16 𝛼 𝛼 X iajs-2566 252 17 , , PUNCT iajs-2566 252 18 𝛼 𝛼 NOUN iajs-2566 252 19 ) ) PUNCT iajs-2566 252 20 ] ] PUNCT iajs-2566 252 21 = = SYM iajs-2566 252 22 0 0 NUM iajs-2566 252 23 β‡’π‘™π‘–π‘šπ‘› β‡’π‘™π‘–π‘šπ‘› PROPN iajs-2566 252 24 π‘šβ†’βˆž π‘šβ†’βˆž NUM iajs-2566 252 25 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 252 26 , , PUNCT iajs-2566 252 27 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 252 28 , , PUNCT iajs-2566 252 29 𝛼 𝛼 NOUN iajs-2566 252 30 ) ) PUNCT iajs-2566 252 31 = = PUNCT iajs-2566 252 32 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 252 33 , , PUNCT iajs-2566 252 34 𝛼 𝛼 INTJ iajs-2566 252 35 , , PUNCT iajs-2566 252 36 𝛼 𝛼 NOUN iajs-2566 252 37 ) ) PUNCT iajs-2566 252 38 hence hence ADV iajs-2566 252 39 ( ( PUNCT iajs-2566 252 40 π‘Œ π‘Œ PROPN iajs-2566 252 41 , , PUNCT iajs-2566 252 42 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 252 43 ) ) PUNCT iajs-2566 252 44 is be AUX iajs-2566 252 45 converge converge VERB iajs-2566 252 46 thus thus ADV iajs-2566 252 47 ( ( PUNCT iajs-2566 252 48 π‘Œ π‘Œ PROPN iajs-2566 252 49 , , PUNCT iajs-2566 252 50 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 252 51 ) ) PUNCT iajs-2566 252 52 is be AUX iajs-2566 252 53 complete complete ADJ iajs-2566 252 54 . . PUNCT iajs-2566 253 1 corollary corollary ADJ iajs-2566 253 2 17 17 NUM iajs-2566 253 3 we we PRON iajs-2566 253 4 can can AUX iajs-2566 253 5 get get VERB iajs-2566 253 6 from from ADP iajs-2566 253 7 the the DET iajs-2566 253 8 proof proof NOUN iajs-2566 253 9 of of ADP iajs-2566 253 10 theorem theorem ADJ iajs-2566 253 11 16 16 NUM iajs-2566 253 12 , , PUNCT iajs-2566 253 13 ( ( PUNCT iajs-2566 253 14 𝑖𝑖 𝑖𝑖 NOUN iajs-2566 253 15 ) ) PUNCT iajs-2566 253 16 , , PUNCT iajs-2566 254 1 π‘™π‘–π‘šπ‘›,π‘š π‘™π‘–π‘šπ‘›,π‘š NUM iajs-2566 254 2 β†’βˆž[𝐷𝑝(𝛼𝑛 β†’βˆž[𝐷𝑝(𝛼𝑛 SYM iajs-2566 254 3 , , PUNCT iajs-2566 254 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 254 5 , , PUNCT iajs-2566 254 6 𝛼 𝛼 NOUN iajs-2566 254 7 ) ) PUNCT iajs-2566 254 8 βˆ’ βˆ’ PROPN iajs-2566 255 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 255 2 , , PUNCT iajs-2566 255 3 𝛼 𝛼 PROPN iajs-2566 255 4 , , PUNCT iajs-2566 255 5 𝛼)]=π‘™π‘–π‘šπ‘› 𝛼)]=π‘™π‘–π‘šπ‘› PROPN iajs-2566 255 6 , , PUNCT iajs-2566 255 7 π‘š π‘š ADP iajs-2566 255 8 β†’βˆž)[𝐷𝑝(𝛼𝑛 β†’βˆž)[𝐷𝑝(𝛼𝑛 NOUN iajs-2566 255 9 , , PUNCT iajs-2566 255 10 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 255 11 , , PUNCT iajs-2566 255 12 𝛼 𝛼 NOUN iajs-2566 255 13 ) ) PUNCT iajs-2566 255 14 – – PUNCT iajs-2566 255 15 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 255 16 , , PUNCT iajs-2566 255 17 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 255 18 , , PUNCT iajs-2566 255 19 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 255 20 ) ) PUNCT iajs-2566 255 21 ] ] PUNCT iajs-2566 256 1 = = PUNCT iajs-2566 256 2 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 256 3 , , PUNCT iajs-2566 256 4 π‘š π‘š PROPN iajs-2566 256 5 β†’βˆž[𝐷𝑝(𝛼𝑛 β†’βˆž[𝐷𝑝(𝛼𝑛 PROPN iajs-2566 256 6 , , PUNCT iajs-2566 256 7 π›Όπ‘šπ›Ό π›Όπ‘šπ›Ό ADJ iajs-2566 256 8 ) ) PUNCT iajs-2566 256 9 – – PUNCT iajs-2566 256 10 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 256 11 , , PUNCT iajs-2566 256 12 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 256 13 , , PUNCT iajs-2566 256 14 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 256 15 ) ) PUNCT iajs-2566 256 16 ] ] PUNCT iajs-2566 257 1 = = PUNCT iajs-2566 257 2 0 0 NUM iajs-2566 257 3 , , PUNCT iajs-2566 257 4 such such ADJ iajs-2566 257 5 that that SCONJ iajs-2566 257 6 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 257 7 , , PUNCT iajs-2566 257 8 π‘š π‘š X iajs-2566 257 9 β†’βˆž β†’βˆž X iajs-2566 257 10 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 257 11 , , PUNCT iajs-2566 257 12 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 257 13 , , PUNCT iajs-2566 257 14 𝛼 𝛼 NOUN iajs-2566 257 15 ) ) PUNCT iajs-2566 257 16 = = SYM iajs-2566 257 17 π‘™π‘–π‘šπ‘š π‘™π‘–π‘šπ‘š NOUN iajs-2566 257 18 β†’βˆž β†’βˆž NOUN iajs-2566 257 19 ) ) PUNCT iajs-2566 257 20 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 257 21 , , PUNCT iajs-2566 257 22 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 257 23 , , PUNCT iajs-2566 257 24 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 257 25 ) ) PUNCT iajs-2566 257 26 = = PUNCT iajs-2566 257 27 π‘™π‘–π‘šπ‘›β†’βˆž π‘™π‘–π‘šπ‘›β†’βˆž VERB iajs-2566 257 28 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 257 29 , , PUNCT iajs-2566 257 30 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 257 31 , , PUNCT iajs-2566 257 32 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 257 33 ) ) PUNCT iajs-2566 257 34 = = PUNCT iajs-2566 258 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 258 2 , , PUNCT iajs-2566 258 3 𝛼 𝛼 INTJ iajs-2566 258 4 , , PUNCT iajs-2566 258 5 𝛼 𝛼 NOUN iajs-2566 258 6 ) ) PUNCT iajs-2566 258 7 . . PUNCT iajs-2566 259 1 propositions proposition NOUN iajs-2566 259 2 18 18 NUM iajs-2566 259 3 if if SCONJ iajs-2566 259 4 { { PUNCT iajs-2566 259 5 𝛼𝑛 𝛼𝑛 NOUN iajs-2566 259 6 } } PUNCT iajs-2566 259 7 is be AUX iajs-2566 259 8 cauchy cauchy ADJ iajs-2566 259 9 sequence sequence NOUN iajs-2566 259 10 in in ADP iajs-2566 259 11 ( ( PUNCT iajs-2566 259 12 π‘Œ π‘Œ PROPN iajs-2566 259 13 , , PUNCT iajs-2566 259 14 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 259 15 ) ) PUNCT iajs-2566 259 16 , , PUNCT iajs-2566 259 17 then then ADV iajs-2566 259 18 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› PROPN iajs-2566 259 19 , , PUNCT iajs-2566 259 20 π‘š π‘š X iajs-2566 259 21 β†’βˆž β†’βˆž X iajs-2566 259 22 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 PROPN iajs-2566 259 23 , , PUNCT iajs-2566 259 24 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 259 25 , , PUNCT iajs-2566 259 26 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 259 27 ) ) PUNCT iajs-2566 259 28 = = NOUN iajs-2566 259 29 π‘™π‘–π‘šπ‘›β†’βˆž π‘™π‘–π‘šπ‘›β†’βˆž NOUN iajs-2566 259 30 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 259 31 , , PUNCT iajs-2566 259 32 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 259 33 , , PUNCT iajs-2566 259 34 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 259 35 ) ) PUNCT iajs-2566 259 36 . . PUNCT iajs-2566 260 1 proof proof NOUN iajs-2566 260 2 since since SCONJ iajs-2566 260 3 { { PUNCT iajs-2566 260 4 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 260 5 } } PUNCT iajs-2566 260 6 is be AUX iajs-2566 260 7 cauchy cauchy ADJ iajs-2566 260 8 sequence sequence NOUN iajs-2566 260 9 in in ADP iajs-2566 260 10 ( ( PUNCT iajs-2566 260 11 π‘Œ π‘Œ PROPN iajs-2566 260 12 , , PUNCT iajs-2566 260 13 𝐷𝑔 𝐷𝑔 PROPN iajs-2566 260 14 ) ) PUNCT iajs-2566 260 15 then then ADV iajs-2566 260 16 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 260 17 , , PUNCT iajs-2566 260 18 π‘š,π‘™β†’βˆž π‘š,π‘™β†’βˆž NOUN iajs-2566 260 19 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 PRON iajs-2566 260 20 , , PUNCT iajs-2566 260 21 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 260 22 , , PUNCT iajs-2566 260 23 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 260 24 ) ) PUNCT iajs-2566 260 25 = = SYM iajs-2566 261 1 0 0 NUM iajs-2566 261 2 57 57 NUM iajs-2566 261 3 ibn ibn PROPN iajs-2566 261 4 al al PROPN iajs-2566 261 5 - - PUNCT iajs-2566 261 6 haitham haitham PROPN iajs-2566 261 7 jour jour X iajs-2566 261 8 . . PROPN iajs-2566 261 9 for for ADP iajs-2566 261 10 pure pure ADJ iajs-2566 261 11 & & CCONJ iajs-2566 261 12 appl appl PROPN iajs-2566 261 13 . . PUNCT iajs-2566 262 1 sci sci PROPN iajs-2566 262 2 . . PROPN iajs-2566 263 1 34 34 NUM iajs-2566 263 2 ( ( PUNCT iajs-2566 263 3 1 1 NUM iajs-2566 263 4 ) ) PUNCT iajs-2566 263 5 2021 2021 NUM iajs-2566 263 6 and and CCONJ iajs-2566 263 7 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 NOUN iajs-2566 263 8 , , PUNCT iajs-2566 263 9 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 263 10 , , PUNCT iajs-2566 263 11 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 263 12 ) ) PUNCT iajs-2566 263 13 = = SYM iajs-2566 263 14 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 263 15 , , PUNCT iajs-2566 263 16 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 263 17 , , PUNCT iajs-2566 263 18 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 263 19 ) ) PUNCT iajs-2566 263 20 + + CCONJ iajs-2566 263 21 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 263 22 , , PUNCT iajs-2566 263 23 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 263 24 , , PUNCT iajs-2566 263 25 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 263 26 ) ) PUNCT iajs-2566 264 1 + + CCONJ iajs-2566 264 2 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 264 3 , , PUNCT iajs-2566 264 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 264 5 , , PUNCT iajs-2566 264 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 264 7 ) ) PUNCT iajs-2566 264 8 + + CCONJ iajs-2566 264 9 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 264 10 , , PUNCT iajs-2566 264 11 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 264 12 , , PUNCT iajs-2566 264 13 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 264 14 ) ) PUNCT iajs-2566 265 1 + + CCONJ iajs-2566 265 2 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 265 3 , , PUNCT iajs-2566 265 4 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 265 5 , , PUNCT iajs-2566 265 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 265 7 ) ) PUNCT iajs-2566 266 1 + + CCONJ iajs-2566 266 2 𝐷𝑝(𝛼𝑙 𝐷𝑝(𝛼𝑙 NOUN iajs-2566 266 3 , , PUNCT iajs-2566 266 4 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 266 5 , , PUNCT iajs-2566 266 6 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 266 7 ) ) PUNCT iajs-2566 266 8 – – PUNCT iajs-2566 266 9 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 266 10 , , PUNCT iajs-2566 266 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 266 12 , , PUNCT iajs-2566 266 13 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 266 14 ) ) PUNCT iajs-2566 266 15 – – PUNCT iajs-2566 266 16 2𝐷𝑝(π›Όπ‘š 2𝐷𝑝(π›Όπ‘š NUM iajs-2566 266 17 , , PUNCT iajs-2566 266 18 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 266 19 , , PUNCT iajs-2566 266 20 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 266 21 ) ) PUNCT iajs-2566 266 22 – – PUNCT iajs-2566 266 23 2𝐷𝑝(𝛼𝑙 2𝐷𝑝(𝛼𝑙 NUM iajs-2566 266 24 , , PUNCT iajs-2566 266 25 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 266 26 , , PUNCT iajs-2566 266 27 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 266 28 ) ) PUNCT iajs-2566 266 29 . . PUNCT iajs-2566 267 1 and and CCONJ iajs-2566 267 2 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 267 3 , , PUNCT iajs-2566 267 4 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 267 5 , , PUNCT iajs-2566 267 6 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 267 7 ) ) PUNCT iajs-2566 267 8 βˆ’ βˆ’ NOUN iajs-2566 268 1 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 268 2 , , PUNCT iajs-2566 268 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 4 , , PUNCT iajs-2566 268 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 6 ) ) PUNCT iajs-2566 268 7 ≀ ≀ NOUN iajs-2566 268 8 𝐷𝑔(𝛼𝑛 𝐷𝑔(𝛼𝑛 PROPN iajs-2566 268 9 , , PUNCT iajs-2566 268 10 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 11 , , PUNCT iajs-2566 268 12 𝛼𝑙 𝛼𝑙 NOUN iajs-2566 268 13 ) ) PUNCT iajs-2566 268 14 then then ADV iajs-2566 268 15 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› PROPN iajs-2566 268 16 , , PUNCT iajs-2566 268 17 π‘š π‘š PROPN iajs-2566 268 18 β†’βˆžπ·π‘(𝛼𝑛 β†’βˆžπ·π‘(𝛼𝑛 PROPN iajs-2566 268 19 , , PUNCT iajs-2566 268 20 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 21 , , PUNCT iajs-2566 268 22 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 23 ) ) PUNCT iajs-2566 268 24 – – PUNCT iajs-2566 268 25 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 268 26 , , PUNCT iajs-2566 268 27 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 28 , , PUNCT iajs-2566 268 29 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 30 ) ) PUNCT iajs-2566 268 31 β†’ β†’ SYM iajs-2566 268 32 0 0 NUM iajs-2566 268 33 similarly similarly ADV iajs-2566 268 34 π‘™π‘–π‘šπ‘› π‘™π‘–π‘šπ‘› NOUN iajs-2566 268 35 , , PUNCT iajs-2566 268 36 π‘š π‘š PROPN iajs-2566 268 37 β†’βˆžπ·π‘ β†’βˆžπ·π‘ PROPN iajs-2566 268 38 ( ( PUNCT iajs-2566 268 39 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 40 , , PUNCT iajs-2566 268 41 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 42 , , PUNCT iajs-2566 268 43 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 44 ) ) PUNCT iajs-2566 268 45 – – PUNCT iajs-2566 268 46 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 268 47 , , PUNCT iajs-2566 268 48 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 49 , , PUNCT iajs-2566 268 50 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 268 51 ) ) PUNCT iajs-2566 268 52 β†’ β†’ SYM iajs-2566 268 53 0 0 NUM iajs-2566 268 54 since since SCONJ iajs-2566 268 55 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 268 56 , , PUNCT iajs-2566 268 57 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 58 , , PUNCT iajs-2566 268 59 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 268 60 ) ) PUNCT iajs-2566 268 61 – – PUNCT iajs-2566 268 62 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 268 63 , , PUNCT iajs-2566 268 64 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 65 , , PUNCT iajs-2566 268 66 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 268 67 ) ) PUNCT iajs-2566 269 1 = = SYM iajs-2566 269 2 𝐷𝑝(π›Όπ‘š 𝐷𝑝(π›Όπ‘š PROPN iajs-2566 269 3 , , PUNCT iajs-2566 269 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 269 5 , , PUNCT iajs-2566 269 6 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 269 7 ) ) PUNCT iajs-2566 269 8 + + CCONJ iajs-2566 269 9 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 269 10 , , PUNCT iajs-2566 269 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 12 , , PUNCT iajs-2566 269 13 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 269 14 ) ) PUNCT iajs-2566 269 15 βˆ’ βˆ’ NOUN iajs-2566 269 16 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 269 17 , , PUNCT iajs-2566 269 18 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 19 , , PUNCT iajs-2566 269 20 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 269 21 ) ) PUNCT iajs-2566 269 22 βˆ’ βˆ’ NOUN iajs-2566 269 23 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 269 24 , , PUNCT iajs-2566 269 25 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 26 , , PUNCT iajs-2566 269 27 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 28 ) ) PUNCT iajs-2566 269 29 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› VERB iajs-2566 269 30 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(π›Όπ‘š π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(π›Όπ‘š NOUN iajs-2566 269 31 , , PUNCT iajs-2566 269 32 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 269 33 , , PUNCT iajs-2566 269 34 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 269 35 ) ) PUNCT iajs-2566 269 36 βˆ’ βˆ’ NOUN iajs-2566 269 37 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 269 38 , , PUNCT iajs-2566 269 39 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 40 , , PUNCT iajs-2566 269 41 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 269 42 ) ) PUNCT iajs-2566 269 43 ] ] PUNCT iajs-2566 270 1 = = PUNCT iajs-2566 270 2 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(π›Όπ‘š π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(π›Όπ‘š PROPN iajs-2566 270 3 , , PUNCT iajs-2566 270 4 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 270 5 , , PUNCT iajs-2566 270 6 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 270 7 ) ) PUNCT iajs-2566 270 8 βˆ’ βˆ’ NOUN iajs-2566 270 9 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 270 10 , , PUNCT iajs-2566 270 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 270 12 , , PUNCT iajs-2566 270 13 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 270 14 ) ) PUNCT iajs-2566 270 15 ] ] PUNCT iajs-2566 271 1 + + PUNCT iajs-2566 271 2 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(𝛼𝑛 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝(𝛼𝑛 NUM iajs-2566 271 3 , , PUNCT iajs-2566 271 4 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 271 5 , , PUNCT iajs-2566 271 6 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 271 7 ) ) PUNCT iajs-2566 271 8 βˆ’ βˆ’ NOUN iajs-2566 271 9 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 271 10 , , PUNCT iajs-2566 271 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 271 12 , , PUNCT iajs-2566 271 13 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 271 14 ) ) PUNCT iajs-2566 271 15 ] ] PUNCT iajs-2566 271 16 ⟢ ⟢ NOUN iajs-2566 271 17 0 0 PUNCT iajs-2566 271 18 so so SCONJ iajs-2566 271 19 that that SCONJ iajs-2566 271 20 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž[𝐷𝑝 NOUN iajs-2566 271 21 ( ( PUNCT iajs-2566 271 22 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 271 23 , , PUNCT iajs-2566 271 24 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 271 25 , , PUNCT iajs-2566 271 26 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 271 27 ) ) PUNCT iajs-2566 271 28 βˆ’ βˆ’ PROPN iajs-2566 272 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 272 2 ( ( PUNCT iajs-2566 272 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 272 4 , , PUNCT iajs-2566 272 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 272 6 , , PUNCT iajs-2566 272 7 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 272 8 ) ) PUNCT iajs-2566 272 9 ] ] PUNCT iajs-2566 272 10 ⟢ ⟢ NOUN iajs-2566 272 11 0 0 NUM iajs-2566 272 12 let let VERB iajs-2566 272 13 𝛼𝑛 𝛼𝑛 INTJ iajs-2566 272 14 = = SYM iajs-2566 273 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 273 2 ( ( PUNCT iajs-2566 273 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 4 , , PUNCT iajs-2566 273 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 6 , , PUNCT iajs-2566 273 7 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 8 ) ) PUNCT iajs-2566 273 9 ∴ ∴ PROPN iajs-2566 273 10 | | ADV iajs-2566 273 11 π›Όπ‘š π›Όπ‘š VERB iajs-2566 273 12 – – PUNCT iajs-2566 273 13 𝛼𝑛| 𝛼𝑛| NOUN iajs-2566 273 14 β†’ β†’ SYM iajs-2566 273 15 0 0 PROPN iajs-2566 273 16 π‘Žπ‘  π‘Žπ‘  PROPN iajs-2566 273 17 𝑛 𝑛 PROPN iajs-2566 273 18 , , PUNCT iajs-2566 273 19 π‘š π‘š PROPN iajs-2566 273 20 ⟢ ⟢ NOUN iajs-2566 273 21 ∞ ∞ NUM iajs-2566 273 22 hence hence ADV iajs-2566 273 23 { { PUNCT iajs-2566 273 24 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 25 } } PUNCT iajs-2566 273 26 is be AUX iajs-2566 273 27 a a DET iajs-2566 273 28 cauchy cauchy ADJ iajs-2566 273 29 sequence sequence NOUN iajs-2566 273 30 in in ADP iajs-2566 273 31 r r NOUN iajs-2566 273 32 , , PUNCT iajs-2566 273 33 therefor therefor ADP iajs-2566 273 34 { { PUNCT iajs-2566 273 35 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 273 36 , , PUNCT iajs-2566 273 37 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 38 , , PUNCT iajs-2566 273 39 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 273 40 ) ) PUNCT iajs-2566 273 41 } } PUNCT iajs-2566 273 42 converge converge VERB iajs-2566 273 43 to to ADP iajs-2566 273 44 Ξ± Ξ± NOUN iajs-2566 273 45 . . PUNCT iajs-2566 274 1 also also ADV iajs-2566 274 2 , , PUNCT iajs-2566 274 3 π‘™π‘–π‘šπ‘›βŸΆβˆž π‘™π‘–π‘šπ‘›βŸΆβˆž ADV iajs-2566 274 4 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 274 5 , , PUNCT iajs-2566 274 6 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 274 7 , , PUNCT iajs-2566 274 8 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 274 9 ) ) PUNCT iajs-2566 274 10 = = SYM iajs-2566 274 11 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆž PROPN iajs-2566 275 1 [ [ X iajs-2566 275 2 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 275 3 , , PUNCT iajs-2566 275 4 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 5 , , PUNCT iajs-2566 275 6 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 275 7 ) ) PUNCT iajs-2566 275 8 + + CCONJ iajs-2566 275 9 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 275 10 , , PUNCT iajs-2566 275 11 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 12 , , PUNCT iajs-2566 275 13 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 14 ) ) PUNCT iajs-2566 275 15 – – PUNCT iajs-2566 275 16 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 275 17 , , PUNCT iajs-2566 275 18 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 19 , , PUNCT iajs-2566 275 20 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 21 ) ) PUNCT iajs-2566 275 22 ] ] PUNCT iajs-2566 275 23 then then ADV iajs-2566 275 24 [ [ X iajs-2566 275 25 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 275 26 ( ( PUNCT iajs-2566 275 27 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 28 , , PUNCT iajs-2566 275 29 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 30 , , PUNCT iajs-2566 275 31 π›Όπ‘š π›Όπ‘š NOUN iajs-2566 275 32 ) ) PUNCT iajs-2566 275 33 – – PUNCT iajs-2566 275 34 𝐷𝑝(𝛼𝑛 𝐷𝑝(𝛼𝑛 NOUN iajs-2566 275 35 , , PUNCT iajs-2566 275 36 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 37 , , PUNCT iajs-2566 275 38 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 39 ) ) PUNCT iajs-2566 275 40 ] ] PUNCT iajs-2566 275 41 ⟢ ⟢ NOUN iajs-2566 275 42 0 0 NUM iajs-2566 275 43 so so ADV iajs-2566 275 44 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆžπ·π‘(𝛼𝑛 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆžπ·π‘(𝛼𝑛 PROPN iajs-2566 275 45 , , PUNCT iajs-2566 275 46 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 47 , , PUNCT iajs-2566 275 48 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 275 49 ) ) PUNCT iajs-2566 275 50 = = SYM iajs-2566 275 51 𝛼 𝛼 PROPN iajs-2566 275 52 thus thus ADV iajs-2566 275 53 π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆžπ·π‘ π‘™π‘–π‘šπ‘›,π‘šβŸΆβˆžπ·π‘ X iajs-2566 275 54 ( ( PUNCT iajs-2566 275 55 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 56 , , PUNCT iajs-2566 275 57 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 275 58 , , PUNCT iajs-2566 275 59 π›Όπ‘š π›Όπ‘š PROPN iajs-2566 275 60 ) ) PUNCT iajs-2566 275 61 = = SYM iajs-2566 276 1 π‘™π‘–π‘šπ‘›βŸΆβˆžπ·π‘(𝛼𝑛 π‘™π‘–π‘šπ‘›βŸΆβˆžπ·π‘(𝛼𝑛 PROPN iajs-2566 276 2 , , PUNCT iajs-2566 276 3 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 276 4 , , PUNCT iajs-2566 276 5 𝛼𝑛 𝛼𝑛 PROPN iajs-2566 276 6 ) ) PUNCT iajs-2566 276 7 . . PUNCT iajs-2566 277 1 βŽ• βŽ• PROPN iajs-2566 277 2 theorem theorem VERB iajs-2566 277 3 19 19 NUM iajs-2566 277 4 if if SCONJ iajs-2566 277 5 ( ( PUNCT iajs-2566 277 6 y y PROPN iajs-2566 277 7 , , PUNCT iajs-2566 277 8 𝑝 𝑝 NOUN iajs-2566 277 9 ) ) PUNCT iajs-2566 277 10 be be AUX iajs-2566 277 11 partial partial ADJ iajs-2566 277 12 metric metric ADJ iajs-2566 277 13 space space NOUN iajs-2566 277 14 then then ADV iajs-2566 277 15 𝐷𝑝(𝛼 𝐷𝑝(𝛼 VERB iajs-2566 277 16 , , PUNCT iajs-2566 277 17 𝛽 𝛽 NOUN iajs-2566 277 18 , , PUNCT iajs-2566 277 19 𝛾 𝛾 NOUN iajs-2566 277 20 ) ) PUNCT iajs-2566 277 21 = = SYM iajs-2566 277 22 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 277 23 , , PUNCT iajs-2566 277 24 𝛽 𝛽 NOUN iajs-2566 277 25 ) ) PUNCT iajs-2566 278 1 + + X iajs-2566 278 2 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 278 3 , , PUNCT iajs-2566 278 4 𝛾 𝛾 PROPN iajs-2566 278 5 ) ) PUNCT iajs-2566 279 1 + + NUM iajs-2566 279 2 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 279 3 , , PUNCT iajs-2566 279 4 𝛾 𝛾 NOUN iajs-2566 279 5 ) ) PUNCT iajs-2566 279 6 – – PUNCT iajs-2566 279 7 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 279 8 , , PUNCT iajs-2566 279 9 𝛼 𝛼 NOUN iajs-2566 279 10 ) ) PUNCT iajs-2566 279 11 – – PUNCT iajs-2566 279 12 𝛲(𝛽 𝛲(𝛽 PUNCT iajs-2566 279 13 , , PUNCT iajs-2566 279 14 𝛽 𝛽 NOUN iajs-2566 279 15 ) ) PUNCT iajs-2566 279 16 – – PUNCT iajs-2566 279 17 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 279 18 , , PUNCT iajs-2566 279 19 𝛾 𝛾 PROPN iajs-2566 279 20 ) ) PUNCT iajs-2566 279 21 ( ( PUNCT iajs-2566 279 22 1.3 1.3 NUM iajs-2566 279 23 ) ) PUNCT iajs-2566 279 24 is be AUX iajs-2566 279 25 general general ADJ iajs-2566 279 26 partial partial ADJ iajs-2566 279 27 metric metric ADJ iajs-2566 279 28 space space NOUN iajs-2566 279 29 . . PUNCT iajs-2566 280 1 1)𝑆𝑖𝑛𝑐𝑒 1)𝑆𝑖𝑛𝑐𝑒 PROPN iajs-2566 280 2 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 280 3 , , PUNCT iajs-2566 280 4 𝛽 𝛽 NOUN iajs-2566 280 5 ) ) PUNCT iajs-2566 280 6 – – PUNCT iajs-2566 280 7 𝑝 𝑝 NOUN iajs-2566 280 8 ( ( PUNCT iajs-2566 280 9 𝛼 𝛼 PROPN iajs-2566 280 10 , , PUNCT iajs-2566 280 11 𝛼 𝛼 NOUN iajs-2566 280 12 ) ) PUNCT iajs-2566 280 13 β‰₯ β‰₯ NOUN iajs-2566 280 14 0 0 NUM iajs-2566 280 15 , , PUNCT iajs-2566 280 16 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 280 17 , , PUNCT iajs-2566 280 18 𝛾 𝛾 PROPN iajs-2566 280 19 ) ) PUNCT iajs-2566 280 20 – – PUNCT iajs-2566 280 21 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 280 22 , , PUNCT iajs-2566 280 23 𝛾 𝛾 PROPN iajs-2566 280 24 ) ) PUNCT iajs-2566 280 25 β‰₯ β‰₯ NOUN iajs-2566 280 26 0 0 NUM iajs-2566 280 27 , , PUNCT iajs-2566 280 28 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 280 29 , , PUNCT iajs-2566 280 30 𝛾 𝛾 NOUN iajs-2566 280 31 ) ) PUNCT iajs-2566 280 32 – – PUNCT iajs-2566 280 33 𝑝 𝑝 NOUN iajs-2566 280 34 ( ( PUNCT iajs-2566 280 35 𝛽 𝛽 PROPN iajs-2566 280 36 , , PUNCT iajs-2566 280 37 𝛽 𝛽 NOUN iajs-2566 280 38 ) ) PUNCT iajs-2566 280 39 β‰₯ β‰₯ NOUN iajs-2566 280 40 0 0 NUM iajs-2566 281 1 then then ADV iajs-2566 281 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 281 3 ( ( PUNCT iajs-2566 281 4 𝛼 𝛼 INTJ iajs-2566 281 5 , , PUNCT iajs-2566 281 6 𝛽 𝛽 NOUN iajs-2566 281 7 , , PUNCT iajs-2566 281 8 𝛾 𝛾 PROPN iajs-2566 281 9 ) ) PUNCT iajs-2566 281 10 β‰₯ β‰₯ NOUN iajs-2566 281 11 0 0 NUM iajs-2566 281 12 2)𝑙𝑒𝑑 2)𝑙𝑒𝑑 NUM iajs-2566 282 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 282 2 ( ( PUNCT iajs-2566 282 3 𝛼 𝛼 INTJ iajs-2566 282 4 , , PUNCT iajs-2566 282 5 𝛽 𝛽 NOUN iajs-2566 282 6 , , PUNCT iajs-2566 282 7 𝛾 𝛾 NOUN iajs-2566 282 8 ) ) PUNCT iajs-2566 282 9 = = SYM iajs-2566 283 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 283 2 ( ( PUNCT iajs-2566 283 3 𝛼 𝛼 INTJ iajs-2566 283 4 , , PUNCT iajs-2566 283 5 𝛼 𝛼 INTJ iajs-2566 283 6 , , PUNCT iajs-2566 283 7 𝛼 𝛼 NOUN iajs-2566 283 8 ) ) PUNCT iajs-2566 283 9 = = SYM iajs-2566 284 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 284 2 ( ( PUNCT iajs-2566 284 3 𝛽 𝛽 PROPN iajs-2566 284 4 , , PUNCT iajs-2566 284 5 𝛽 𝛽 PROPN iajs-2566 284 6 , , PUNCT iajs-2566 284 7 𝛽 𝛽 NOUN iajs-2566 284 8 ) ) PUNCT iajs-2566 284 9 = = SYM iajs-2566 284 10 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 284 11 , , PUNCT iajs-2566 284 12 𝛾 𝛾 NOUN iajs-2566 284 13 , , PUNCT iajs-2566 284 14 𝛾 𝛾 NOUN iajs-2566 284 15 ) ) PUNCT iajs-2566 284 16 𝑠𝑖𝑛𝑐𝑒 𝑠𝑖𝑛𝑐𝑒 VERB iajs-2566 284 17 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 284 18 , , PUNCT iajs-2566 284 19 𝛼 𝛼 INTJ iajs-2566 284 20 , , PUNCT iajs-2566 284 21 𝛼 𝛼 NOUN iajs-2566 284 22 ) ) PUNCT iajs-2566 284 23 = = SYM iajs-2566 285 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 285 2 ( ( PUNCT iajs-2566 285 3 𝛽 𝛽 PROPN iajs-2566 285 4 , , PUNCT iajs-2566 285 5 𝛽 𝛽 PROPN iajs-2566 285 6 , , PUNCT iajs-2566 285 7 𝛽 𝛽 NOUN iajs-2566 285 8 ) ) PUNCT iajs-2566 285 9 = = SYM iajs-2566 286 1 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 286 2 , , PUNCT iajs-2566 286 3 𝛾 𝛾 NOUN iajs-2566 286 4 , , PUNCT iajs-2566 286 5 𝛾 𝛾 NOUN iajs-2566 286 6 ) ) PUNCT iajs-2566 286 7 = = SYM iajs-2566 286 8 0 0 NUM iajs-2566 286 9 β‡’ β‡’ PROPN iajs-2566 286 10 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 286 11 ( ( PUNCT iajs-2566 286 12 𝛼 𝛼 INTJ iajs-2566 286 13 , , PUNCT iajs-2566 286 14 𝛽 𝛽 PROPN iajs-2566 286 15 , , PUNCT iajs-2566 286 16 𝛾 𝛾 NOUN iajs-2566 286 17 ) ) PUNCT iajs-2566 286 18 = = SYM iajs-2566 286 19 0 0 NUM iajs-2566 286 20 β‡’ β‡’ PROPN iajs-2566 286 21 𝑝 𝑝 PROPN iajs-2566 286 22 ( ( PUNCT iajs-2566 286 23 𝛼 𝛼 PROPN iajs-2566 286 24 , , PUNCT iajs-2566 286 25 𝛽 𝛽 NOUN iajs-2566 286 26 ) ) PUNCT iajs-2566 287 1 + + X iajs-2566 287 2 𝑝 𝑝 NOUN iajs-2566 287 3 ( ( PUNCT iajs-2566 287 4 𝛽 𝛽 NOUN iajs-2566 287 5 , , PUNCT iajs-2566 287 6 𝛾 𝛾 PROPN iajs-2566 287 7 ) ) PUNCT iajs-2566 287 8 + + X iajs-2566 288 1 𝑝 𝑝 NOUN iajs-2566 288 2 ( ( PUNCT iajs-2566 288 3 𝛼 𝛼 NOUN iajs-2566 288 4 , , PUNCT iajs-2566 288 5 𝛾 𝛾 NOUN iajs-2566 288 6 ) ) PUNCT iajs-2566 288 7 – – PUNCT iajs-2566 288 8 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 288 9 , , PUNCT iajs-2566 288 10 𝛼 𝛼 NOUN iajs-2566 288 11 ) ) PUNCT iajs-2566 288 12 – – PUNCT iajs-2566 288 13 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 288 14 , , PUNCT iajs-2566 288 15 𝛽 𝛽 NOUN iajs-2566 288 16 ) ) PUNCT iajs-2566 288 17 – – PUNCT iajs-2566 288 18 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 288 19 , , PUNCT iajs-2566 288 20 𝛾 𝛾 NOUN iajs-2566 288 21 ) ) PUNCT iajs-2566 288 22 = = SYM iajs-2566 288 23 0 0 NUM iajs-2566 289 1 β‡’ β‡’ PROPN iajs-2566 289 2 𝑝 𝑝 PROPN iajs-2566 289 3 ( ( PUNCT iajs-2566 289 4 𝛼 𝛼 PROPN iajs-2566 289 5 , , PUNCT iajs-2566 289 6 𝛽 𝛽 NOUN iajs-2566 289 7 ) ) PUNCT iajs-2566 289 8 – – PUNCT iajs-2566 289 9 𝑝 𝑝 NOUN iajs-2566 289 10 ( ( PUNCT iajs-2566 289 11 𝛼 𝛼 INTJ iajs-2566 289 12 , , PUNCT iajs-2566 289 13 𝛼 𝛼 NOUN iajs-2566 289 14 ) ) PUNCT iajs-2566 289 15 = = SYM iajs-2566 289 16 0 0 NUM iajs-2566 289 17 β‡’ β‡’ PROPN iajs-2566 289 18 𝑝 𝑝 PROPN iajs-2566 289 19 ( ( PUNCT iajs-2566 289 20 𝛼 𝛼 PROPN iajs-2566 289 21 , , PUNCT iajs-2566 289 22 𝛽 𝛽 NOUN iajs-2566 289 23 ) ) PUNCT iajs-2566 289 24 = = SYM iajs-2566 289 25 𝑝 𝑝 PROPN iajs-2566 289 26 ( ( PUNCT iajs-2566 289 27 𝛼 𝛼 PROPN iajs-2566 289 28 , , PUNCT iajs-2566 289 29 𝛼 𝛼 NOUN iajs-2566 289 30 ) ) PUNCT iajs-2566 289 31 … … PUNCT iajs-2566 289 32 1 1 NUM iajs-2566 289 33 , , PUNCT iajs-2566 289 34 β‡’ β‡’ PROPN iajs-2566 289 35 𝑝 𝑝 PROPN iajs-2566 289 36 ( ( PUNCT iajs-2566 289 37 𝛼 𝛼 INTJ iajs-2566 289 38 , , PUNCT iajs-2566 289 39 𝛾 𝛾 NOUN iajs-2566 289 40 ) ) PUNCT iajs-2566 289 41 – – PUNCT iajs-2566 289 42 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 289 43 , , PUNCT iajs-2566 289 44 𝛾 𝛾 NOUN iajs-2566 289 45 ) ) PUNCT iajs-2566 289 46 = = SYM iajs-2566 289 47 0 0 NUM iajs-2566 289 48 β‡’ β‡’ PROPN iajs-2566 289 49 𝑝 𝑝 PROPN iajs-2566 289 50 ( ( PUNCT iajs-2566 289 51 𝛼 𝛼 PROPN iajs-2566 289 52 , , PUNCT iajs-2566 289 53 𝛾 𝛾 NOUN iajs-2566 289 54 ) ) PUNCT iajs-2566 289 55 = = SYM iajs-2566 289 56 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 289 57 , , PUNCT iajs-2566 289 58 𝛾 𝛾 NOUN iajs-2566 289 59 ) ) PUNCT iajs-2566 289 60 … … PUNCT iajs-2566 289 61 2 2 NUM iajs-2566 289 62 , , PUNCT iajs-2566 289 63 58 58 NUM iajs-2566 289 64 ibn ibn PROPN iajs-2566 289 65 al al PROPN iajs-2566 289 66 - - PUNCT iajs-2566 289 67 haitham haitham PROPN iajs-2566 289 68 jour jour X iajs-2566 289 69 . . PROPN iajs-2566 290 1 for for ADP iajs-2566 290 2 pure pure ADJ iajs-2566 290 3 & & CCONJ iajs-2566 290 4 appl appl PROPN iajs-2566 290 5 . . PUNCT iajs-2566 291 1 sci sci PROPN iajs-2566 291 2 . . PROPN iajs-2566 292 1 34 34 NUM iajs-2566 292 2 ( ( PUNCT iajs-2566 292 3 1 1 NUM iajs-2566 292 4 ) ) PUNCT iajs-2566 292 5 2021 2021 NUM iajs-2566 292 6 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN iajs-2566 292 7 𝑝 𝑝 PROPN iajs-2566 292 8 ( ( PUNCT iajs-2566 292 9 𝛽 𝛽 NOUN iajs-2566 292 10 , , PUNCT iajs-2566 292 11 𝛾 𝛾 NOUN iajs-2566 292 12 ) ) PUNCT iajs-2566 292 13 – – PUNCT iajs-2566 293 1 𝑝 𝑝 NOUN iajs-2566 293 2 ( ( PUNCT iajs-2566 293 3 𝛽 𝛽 PROPN iajs-2566 293 4 , , PUNCT iajs-2566 293 5 𝛽 𝛽 NOUN iajs-2566 293 6 ) ) PUNCT iajs-2566 293 7 = = SYM iajs-2566 293 8 0 0 NUM iajs-2566 293 9 β‡’ β‡’ PROPN iajs-2566 293 10 𝑝 𝑝 PROPN iajs-2566 293 11 ( ( PUNCT iajs-2566 293 12 𝛽 𝛽 NOUN iajs-2566 293 13 , , PUNCT iajs-2566 293 14 𝛾 𝛾 NOUN iajs-2566 293 15 ) ) PUNCT iajs-2566 293 16 = = SYM iajs-2566 293 17 𝑝 𝑝 PROPN iajs-2566 293 18 ( ( PUNCT iajs-2566 293 19 𝛽 𝛽 PROPN iajs-2566 293 20 , , PUNCT iajs-2566 293 21 𝛽 𝛽 NOUN iajs-2566 293 22 ) ) PUNCT iajs-2566 293 23 … … PUNCT iajs-2566 293 24 3 3 NUM iajs-2566 293 25 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 293 26 1 1 NUM iajs-2566 293 27 𝑝 𝑝 PROPN iajs-2566 293 28 ( ( PUNCT iajs-2566 293 29 𝛼 𝛼 PROPN iajs-2566 293 30 , , PUNCT iajs-2566 293 31 𝛼 𝛼 NOUN iajs-2566 293 32 ) ) PUNCT iajs-2566 293 33 = = SYM iajs-2566 293 34 𝑝 𝑝 PROPN iajs-2566 293 35 ( ( PUNCT iajs-2566 293 36 𝛼 𝛼 PROPN iajs-2566 293 37 , , PUNCT iajs-2566 293 38 𝛽 𝛽 NOUN iajs-2566 293 39 ) ) PUNCT iajs-2566 293 40 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 293 41 𝑏𝑦 𝑏𝑦 PROPN iajs-2566 293 42 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› PROPN iajs-2566 293 43 𝑝 𝑝 PROPN iajs-2566 293 44 ( ( PUNCT iajs-2566 293 45 𝛼 𝛼 PROPN iajs-2566 293 46 , , PUNCT iajs-2566 293 47 𝛼 𝛼 NOUN iajs-2566 293 48 ) ) PUNCT iajs-2566 293 49 = = SYM iajs-2566 293 50 𝑝 𝑝 PROPN iajs-2566 293 51 ( ( PUNCT iajs-2566 293 52 𝛼 𝛼 PROPN iajs-2566 293 53 , , PUNCT iajs-2566 293 54 𝛽 𝛽 NOUN iajs-2566 293 55 ) ) PUNCT iajs-2566 293 56 ≀ ≀ NOUN iajs-2566 293 57 𝑝 𝑝 PROPN iajs-2566 293 58 ( ( PUNCT iajs-2566 293 59 𝛼 𝛼 PROPN iajs-2566 293 60 , , PUNCT iajs-2566 293 61 𝛾 𝛾 NOUN iajs-2566 293 62 ) ) PUNCT iajs-2566 293 63 + + CCONJ iajs-2566 293 64 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 293 65 , , PUNCT iajs-2566 293 66 𝛽 𝛽 NOUN iajs-2566 293 67 ) ) PUNCT iajs-2566 293 68 βˆ’ βˆ’ PROPN iajs-2566 293 69 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 293 70 , , PUNCT iajs-2566 293 71 𝛾 𝛾 NOUN iajs-2566 293 72 ) ) PUNCT iajs-2566 293 73 𝑆𝑖𝑛𝑐𝑒 𝑆𝑖𝑛𝑐𝑒 PROPN iajs-2566 293 74 𝑝 𝑝 PROPN iajs-2566 293 75 ( ( PUNCT iajs-2566 293 76 𝛼 𝛼 PROPN iajs-2566 293 77 , , PUNCT iajs-2566 293 78 𝛾 𝛾 NOUN iajs-2566 293 79 ) ) PUNCT iajs-2566 293 80 = = SYM iajs-2566 293 81 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 293 82 , , PUNCT iajs-2566 293 83 𝛾 𝛾 NOUN iajs-2566 293 84 ) ) PUNCT iajs-2566 293 85 & & CCONJ iajs-2566 293 86 𝑝 𝑝 PROPN iajs-2566 293 87 ( ( PUNCT iajs-2566 293 88 𝛽 𝛽 NOUN iajs-2566 293 89 , , PUNCT iajs-2566 293 90 𝛾 𝛾 NOUN iajs-2566 293 91 ) ) PUNCT iajs-2566 293 92 = = SYM iajs-2566 293 93 𝑝 𝑝 PROPN iajs-2566 293 94 ( ( PUNCT iajs-2566 293 95 𝛽 𝛽 PROPN iajs-2566 293 96 , , PUNCT iajs-2566 293 97 𝛽 𝛽 NOUN iajs-2566 293 98 ) ) PUNCT iajs-2566 293 99 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 293 100 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 293 101 𝑝 𝑝 PROPN iajs-2566 293 102 ( ( PUNCT iajs-2566 293 103 𝛼 𝛼 PROPN iajs-2566 293 104 , , PUNCT iajs-2566 293 105 𝛼 𝛼 NOUN iajs-2566 293 106 ) ) PUNCT iajs-2566 293 107 = = SYM iajs-2566 293 108 𝑝 𝑝 PROPN iajs-2566 293 109 ( ( PUNCT iajs-2566 293 110 𝛽 𝛽 PROPN iajs-2566 293 111 , , PUNCT iajs-2566 293 112 𝛽 𝛽 NOUN iajs-2566 293 113 ) ) PUNCT iajs-2566 293 114 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 293 115 2 2 NUM iajs-2566 293 116 𝑝 𝑝 PROPN iajs-2566 293 117 ( ( PUNCT iajs-2566 293 118 𝛽 𝛽 PROPN iajs-2566 293 119 , , PUNCT iajs-2566 293 120 𝛽 𝛽 NOUN iajs-2566 293 121 ) ) PUNCT iajs-2566 293 122 = = SYM iajs-2566 293 123 𝑝 𝑝 PROPN iajs-2566 293 124 ( ( PUNCT iajs-2566 293 125 𝛽 𝛽 NOUN iajs-2566 293 126 , , PUNCT iajs-2566 293 127 𝛾 𝛾 NOUN iajs-2566 293 128 ) ) PUNCT iajs-2566 293 129 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2566 293 130 𝑏𝑦 𝑏𝑦 PROPN iajs-2566 293 131 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› PROPN iajs-2566 293 132 𝑝 𝑝 PROPN iajs-2566 293 133 ( ( PUNCT iajs-2566 293 134 𝛽 𝛽 PROPN iajs-2566 293 135 , , PUNCT iajs-2566 293 136 𝛽 𝛽 NOUN iajs-2566 293 137 ) ) PUNCT iajs-2566 293 138 = = SYM iajs-2566 293 139 𝑝 𝑝 PROPN iajs-2566 293 140 ( ( PUNCT iajs-2566 293 141 𝛽 𝛽 NOUN iajs-2566 293 142 , , PUNCT iajs-2566 293 143 𝛾 𝛾 NOUN iajs-2566 293 144 ) ) PUNCT iajs-2566 293 145 ≀ ≀ NOUN iajs-2566 293 146 𝑝 𝑝 PROPN iajs-2566 293 147 ( ( PUNCT iajs-2566 293 148 𝛽 𝛽 PROPN iajs-2566 293 149 , , PUNCT iajs-2566 293 150 𝛼 𝛼 NOUN iajs-2566 293 151 ) ) PUNCT iajs-2566 293 152 + + X iajs-2566 293 153 𝑝 𝑝 NOUN iajs-2566 293 154 ( ( PUNCT iajs-2566 293 155 𝛼 𝛼 NOUN iajs-2566 293 156 , , PUNCT iajs-2566 293 157 𝛾 𝛾 NOUN iajs-2566 293 158 ) ) PUNCT iajs-2566 293 159 βˆ’ βˆ’ PROPN iajs-2566 293 160 𝑝 𝑝 PROPN iajs-2566 293 161 ( ( PUNCT iajs-2566 293 162 𝛼 𝛼 PROPN iajs-2566 293 163 , , PUNCT iajs-2566 293 164 𝛼 𝛼 NOUN iajs-2566 293 165 ) ) PUNCT iajs-2566 293 166 𝑏𝛽 𝑏𝛽 ADP iajs-2566 293 167 1&2 1&2 NUM iajs-2566 293 168 𝑀𝑒 𝑀𝑒 NOUN iajs-2566 293 169 𝑔𝑒𝑑 𝑔𝑒𝑑 NOUN iajs-2566 293 170 𝑝(𝛽 𝑝(𝛽 PROPN iajs-2566 293 171 , , PUNCT iajs-2566 293 172 𝛽 𝛽 NOUN iajs-2566 293 173 ) ) PUNCT iajs-2566 293 174 = = SYM iajs-2566 293 175 ( ( PUNCT iajs-2566 293 176 𝛾 𝛾 NOUN iajs-2566 293 177 , , PUNCT iajs-2566 293 178 𝛾 𝛾 NOUN iajs-2566 293 179 ) ) PUNCT iajs-2566 293 180 πΉπ‘Ÿπ‘œπ‘š πΉπ‘Ÿπ‘œπ‘š PROPN iajs-2566 293 181 3 3 NUM iajs-2566 293 182 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 293 183 , , PUNCT iajs-2566 293 184 𝛾 𝛾 NOUN iajs-2566 293 185 ) ) PUNCT iajs-2566 293 186 = = SYM iajs-2566 293 187 𝑝 𝑝 PROPN iajs-2566 293 188 ( ( PUNCT iajs-2566 293 189 𝛼 𝛼 PROPN iajs-2566 293 190 , , PUNCT iajs-2566 293 191 𝛾)π‘Žπ‘›π‘‘ 𝛾)π‘Žπ‘›π‘‘ PROPN iajs-2566 293 192 𝑏𝑦 𝑏𝑦 PROPN iajs-2566 293 193 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› PROPN iajs-2566 293 194 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 293 195 , , PUNCT iajs-2566 293 196 𝛾 𝛾 NOUN iajs-2566 293 197 ) ) PUNCT iajs-2566 293 198 = = SYM iajs-2566 293 199 𝑝 𝑝 PROPN iajs-2566 293 200 ( ( PUNCT iajs-2566 293 201 𝛼 𝛼 PROPN iajs-2566 293 202 , , PUNCT iajs-2566 293 203 𝛾 𝛾 NOUN iajs-2566 293 204 ) ) PUNCT iajs-2566 293 205 ≀ ≀ NOUN iajs-2566 293 206 𝑝 𝑝 PROPN iajs-2566 293 207 ( ( PUNCT iajs-2566 293 208 𝛼 𝛼 PROPN iajs-2566 293 209 , , PUNCT iajs-2566 293 210 𝛽 𝛽 NOUN iajs-2566 293 211 ) ) PUNCT iajs-2566 293 212 + + X iajs-2566 293 213 𝑝 𝑝 NOUN iajs-2566 293 214 ( ( PUNCT iajs-2566 293 215 𝛽 𝛽 NOUN iajs-2566 293 216 , , PUNCT iajs-2566 293 217 𝛾 𝛾 NOUN iajs-2566 293 218 ) ) PUNCT iajs-2566 293 219 βˆ’ βˆ’ PROPN iajs-2566 293 220 𝑝 𝑝 PROPN iajs-2566 293 221 ( ( PUNCT iajs-2566 293 222 𝛽 𝛽 PROPN iajs-2566 293 223 , , PUNCT iajs-2566 293 224 𝛽 𝛽 NOUN iajs-2566 293 225 ) ) PUNCT iajs-2566 293 226 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 293 227 1&3 1&3 NUM iajs-2566 293 228 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 293 229 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 293 230 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 293 231 , , PUNCT iajs-2566 293 232 𝛾 𝛾 NOUN iajs-2566 293 233 ) ) PUNCT iajs-2566 293 234 = = SYM iajs-2566 293 235 𝑝 𝑝 PROPN iajs-2566 293 236 ( ( PUNCT iajs-2566 293 237 𝛼 𝛼 PROPN iajs-2566 293 238 , , PUNCT iajs-2566 293 239 𝛼 𝛼 NOUN iajs-2566 293 240 ) ) PUNCT iajs-2566 293 241 𝐻𝑒𝑛𝑐𝑒 𝐻𝑒𝑛𝑐𝑒 PROPN iajs-2566 293 242 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 293 243 , , PUNCT iajs-2566 293 244 𝛼 𝛼 NOUN iajs-2566 293 245 ) ) PUNCT iajs-2566 293 246 = = SYM iajs-2566 293 247 𝑝 𝑝 PROPN iajs-2566 293 248 ( ( PUNCT iajs-2566 293 249 𝛽 𝛽 PROPN iajs-2566 293 250 , , PUNCT iajs-2566 293 251 𝛽 𝛽 NOUN iajs-2566 293 252 ) ) PUNCT iajs-2566 293 253 = = SYM iajs-2566 293 254 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 293 255 , , PUNCT iajs-2566 293 256 𝛾 𝛾 NOUN iajs-2566 293 257 ) ) PUNCT iajs-2566 293 258 π‘‡β„Žπ‘’π‘  π‘‡β„Žπ‘’π‘  PROPN iajs-2566 293 259 𝑝 𝑝 PROPN iajs-2566 293 260 ( ( PUNCT iajs-2566 293 261 𝛼 𝛼 PROPN iajs-2566 293 262 , , PUNCT iajs-2566 293 263 𝛼 𝛼 NOUN iajs-2566 293 264 ) ) PUNCT iajs-2566 293 265 = = SYM iajs-2566 293 266 𝑝 𝑝 PROPN iajs-2566 293 267 ( ( PUNCT iajs-2566 293 268 𝛼 𝛼 PROPN iajs-2566 293 269 , , PUNCT iajs-2566 293 270 𝛽 𝛽 NOUN iajs-2566 293 271 ) ) PUNCT iajs-2566 293 272 = = SYM iajs-2566 293 273 𝑝 𝑝 PROPN iajs-2566 293 274 ( ( PUNCT iajs-2566 293 275 𝛽 𝛽 PROPN iajs-2566 293 276 , , PUNCT iajs-2566 293 277 𝛽 𝛽 NOUN iajs-2566 293 278 ) ) PUNCT iajs-2566 293 279 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 293 280 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› NOUN iajs-2566 293 281 𝛼 𝛼 PROPN iajs-2566 293 282 = = SYM iajs-2566 293 283 𝛽 𝛽 PROPN iajs-2566 293 284 , , PUNCT iajs-2566 293 285 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ PROPN iajs-2566 293 286 𝑝 𝑝 PROPN iajs-2566 293 287 ( ( PUNCT iajs-2566 293 288 𝛽 𝛽 PROPN iajs-2566 293 289 , , PUNCT iajs-2566 293 290 𝛽 𝛽 NOUN iajs-2566 293 291 ) ) PUNCT iajs-2566 293 292 = = SYM iajs-2566 293 293 𝑝 𝑝 PROPN iajs-2566 293 294 ( ( PUNCT iajs-2566 293 295 𝛽 𝛽 NOUN iajs-2566 293 296 , , PUNCT iajs-2566 293 297 𝛾 𝛾 NOUN iajs-2566 293 298 ) ) PUNCT iajs-2566 293 299 = = SYM iajs-2566 293 300 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 293 301 , , PUNCT iajs-2566 293 302 𝛾 𝛾 NOUN iajs-2566 293 303 ) ) PUNCT iajs-2566 293 304 𝑏𝑦 𝑏𝑦 NOUN iajs-2566 293 305 π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› NOUN iajs-2566 293 306 𝛽 𝛽 PROPN iajs-2566 293 307 = = PUNCT iajs-2566 293 308 𝛾 𝛾 NOUN iajs-2566 293 309 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› NOUN iajs-2566 293 310 𝑀𝑒 𝑀𝑒 INTJ iajs-2566 293 311 𝑔𝑒𝑑 𝑔𝑒𝑑 NOUN iajs-2566 293 312 𝛼 𝛼 PROPN iajs-2566 293 313 = = SYM iajs-2566 293 314 𝛽 𝛽 NOUN iajs-2566 293 315 = = SYM iajs-2566 293 316 𝛾. 𝛾. NOUN iajs-2566 293 317 3 3 X iajs-2566 293 318 ) ) PUNCT iajs-2566 293 319 π‘‡π‘Ÿπ‘–π‘£π‘–π‘Žπ‘™ π‘‡π‘Ÿπ‘–π‘£π‘–π‘Žπ‘™ PROPN iajs-2566 293 320 4 4 NUM iajs-2566 293 321 ) ) PUNCT iajs-2566 293 322 𝑠𝑖𝑛𝑐𝑒 𝑠𝑖𝑛𝑐𝑒 PROPN iajs-2566 293 323 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 324 , , PUNCT iajs-2566 293 325 𝛾 𝛾 PROPN iajs-2566 293 326 ) ) PUNCT iajs-2566 293 327 – – PUNCT iajs-2566 293 328 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 293 329 , , PUNCT iajs-2566 293 330 𝛾 𝛾 PROPN iajs-2566 293 331 ) ) PUNCT iajs-2566 293 332 β‰₯ β‰₯ NOUN iajs-2566 293 333 0 0 NUM iajs-2566 293 334 , , PUNCT iajs-2566 293 335 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 336 , , PUNCT iajs-2566 293 337 𝛽 𝛽 PROPN iajs-2566 293 338 ) ) PUNCT iajs-2566 293 339 – – PUNCT iajs-2566 293 340 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 341 , , PUNCT iajs-2566 293 342 πœ‡ πœ‡ ADP iajs-2566 293 343 ) ) PUNCT iajs-2566 293 344 β‰₯ β‰₯ NOUN iajs-2566 293 345 0 0 NUM iajs-2566 293 346 , , PUNCT iajs-2566 293 347 𝑝 𝑝 NOUN iajs-2566 293 348 ( ( PUNCT iajs-2566 293 349 𝛼 𝛼 NOUN iajs-2566 293 350 , , PUNCT iajs-2566 293 351 πœ‡ πœ‡ ADP iajs-2566 293 352 ) ) PUNCT iajs-2566 293 353 – – PUNCT iajs-2566 293 354 𝑝 𝑝 NOUN iajs-2566 293 355 ( ( PUNCT iajs-2566 293 356 𝛼 𝛼 PROPN iajs-2566 293 357 , , PUNCT iajs-2566 293 358 𝛼 𝛼 PROPN iajs-2566 293 359 ) ) PUNCT iajs-2566 293 360 β‰₯ β‰₯ NOUN iajs-2566 293 361 0 0 NUM iajs-2566 293 362 , , PUNCT iajs-2566 293 363 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 364 , , PUNCT iajs-2566 293 365 𝛾 𝛾 PROPN iajs-2566 293 366 ) ) PUNCT iajs-2566 293 367 – – PUNCT iajs-2566 293 368 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 369 , , PUNCT iajs-2566 293 370 πœ‡ πœ‡ ADP iajs-2566 293 371 ) ) PUNCT iajs-2566 293 372 β‰₯ β‰₯ NOUN iajs-2566 293 373 0 0 NUM iajs-2566 293 374 , , PUNCT iajs-2566 293 375 𝑝 𝑝 NOUN iajs-2566 293 376 ( ( PUNCT iajs-2566 293 377 𝛽 𝛽 NOUN iajs-2566 293 378 , , PUNCT iajs-2566 293 379 πœ‡ πœ‡ ADP iajs-2566 293 380 ) ) PUNCT iajs-2566 293 381 – – PUNCT iajs-2566 293 382 𝑝 𝑝 NOUN iajs-2566 293 383 ( ( PUNCT iajs-2566 293 384 𝛽 𝛽 NOUN iajs-2566 293 385 , , PUNCT iajs-2566 293 386 𝛽 𝛽 PROPN iajs-2566 293 387 ) ) PUNCT iajs-2566 293 388 β‰₯ β‰₯ NOUN iajs-2566 293 389 0 0 NUM iajs-2566 293 390 , , PUNCT iajs-2566 293 391 𝑝 𝑝 NOUN iajs-2566 293 392 ( ( PUNCT iajs-2566 293 393 𝛼 𝛼 NOUN iajs-2566 293 394 , , PUNCT iajs-2566 293 395 πœ‡ πœ‡ ADP iajs-2566 293 396 ) ) PUNCT iajs-2566 293 397 – – PUNCT iajs-2566 293 398 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 293 399 , , PUNCT iajs-2566 293 400 πœ‡ πœ‡ ADP iajs-2566 293 401 ) ) PUNCT iajs-2566 293 402 β‰₯ β‰₯ NOUN iajs-2566 293 403 0 0 NUM iajs-2566 293 404 when when SCONJ iajs-2566 293 405 combined combine VERB iajs-2566 293 406 , , PUNCT iajs-2566 293 407 it it PRON iajs-2566 293 408 is be AUX iajs-2566 293 409 more more ADJ iajs-2566 293 410 than than ADP iajs-2566 293 411 and and CCONJ iajs-2566 293 412 equal equal ADJ iajs-2566 293 413 to to ADP iajs-2566 293 414 zero zero NUM iajs-2566 293 415 and and CCONJ iajs-2566 293 416 when when SCONJ iajs-2566 293 417 added add VERB iajs-2566 293 418 these these DET iajs-2566 293 419 values value NOUN iajs-2566 293 420 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 293 421 , , PUNCT iajs-2566 293 422 𝛽 𝛽 NOUN iajs-2566 293 423 ) ) PUNCT iajs-2566 293 424 , , PUNCT iajs-2566 293 425 𝑝 𝑝 PROPN iajs-2566 293 426 ( ( PUNCT iajs-2566 293 427 𝛽 𝛽 PROPN iajs-2566 293 428 , , PUNCT iajs-2566 293 429 𝛾 𝛾 PROPN iajs-2566 293 430 ) ) PUNCT iajs-2566 293 431 , , PUNCT iajs-2566 293 432 𝑝 𝑝 NOUN iajs-2566 293 433 ( ( PUNCT iajs-2566 293 434 𝛼 𝛼 INTJ iajs-2566 293 435 , , PUNCT iajs-2566 293 436 𝛾 𝛾 PROPN iajs-2566 293 437 ) ) PUNCT iajs-2566 293 438 , , PUNCT iajs-2566 293 439 βˆ’ βˆ’ PROPN iajs-2566 293 440 𝑝 𝑝 PROPN iajs-2566 293 441 ( ( PUNCT iajs-2566 293 442 𝛼 𝛼 INTJ iajs-2566 293 443 , , PUNCT iajs-2566 293 444 𝛼 𝛼 NOUN iajs-2566 293 445 ) ) PUNCT iajs-2566 293 446 , , PUNCT iajs-2566 293 447 βˆ’ βˆ’ PROPN iajs-2566 293 448 𝑝 𝑝 PROPN iajs-2566 293 449 ( ( PUNCT iajs-2566 293 450 𝛽 𝛽 PROPN iajs-2566 293 451 , , PUNCT iajs-2566 293 452 𝛽 𝛽 PROPN iajs-2566 293 453 ) ) PUNCT iajs-2566 293 454 , , PUNCT iajs-2566 293 455 βˆ’ βˆ’ PROPN iajs-2566 293 456 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 293 457 , , PUNCT iajs-2566 293 458 𝛾 𝛾 PROPN iajs-2566 293 459 ) ) PUNCT iajs-2566 293 460 π‘‘π‘œ π‘‘π‘œ PRON iajs-2566 293 461 π‘π‘œπ‘‘β„Ž π‘π‘œπ‘‘β„Ž VERB iajs-2566 293 462 π‘ π‘Žπ‘–π‘‘ π‘ π‘Žπ‘–π‘‘ ADJ iajs-2566 293 463 , , PUNCT iajs-2566 293 464 𝑀𝑒 𝑀𝑒 PROPN iajs-2566 293 465 𝑔𝑒𝑑 𝑔𝑒𝑑 PROPN iajs-2566 293 466 𝑝 𝑝 PROPN iajs-2566 293 467 ( ( PUNCT iajs-2566 293 468 𝛼 𝛼 PROPN iajs-2566 293 469 , , PUNCT iajs-2566 293 470 𝛽 𝛽 NOUN iajs-2566 293 471 ) ) PUNCT iajs-2566 294 1 + + X iajs-2566 294 2 𝑝 𝑝 NOUN iajs-2566 294 3 ( ( PUNCT iajs-2566 294 4 𝛽 𝛽 NOUN iajs-2566 294 5 , , PUNCT iajs-2566 294 6 𝛾 𝛾 PROPN iajs-2566 294 7 ) ) PUNCT iajs-2566 294 8 + + X iajs-2566 295 1 𝑝 𝑝 NOUN iajs-2566 295 2 ( ( PUNCT iajs-2566 295 3 𝛼 𝛼 INTJ iajs-2566 295 4 , , PUNCT iajs-2566 295 5 𝛾 𝛾 NOUN iajs-2566 295 6 ) ) PUNCT iajs-2566 295 7 – – PUNCT iajs-2566 295 8 𝑝 𝑝 NOUN iajs-2566 295 9 ( ( PUNCT iajs-2566 295 10 𝛼 𝛼 PROPN iajs-2566 295 11 , , PUNCT iajs-2566 295 12 𝛼 𝛼 NOUN iajs-2566 295 13 ) ) PUNCT iajs-2566 295 14 – – PUNCT iajs-2566 295 15 𝑝 𝑝 NOUN iajs-2566 295 16 ( ( PUNCT iajs-2566 295 17 𝛽 𝛽 PROPN iajs-2566 295 18 , , PUNCT iajs-2566 295 19 𝛽 𝛽 PROPN iajs-2566 295 20 ) ) PUNCT iajs-2566 295 21 – – PUNCT iajs-2566 295 22 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 295 23 , , PUNCT iajs-2566 295 24 𝛾 𝛾 NOUN iajs-2566 295 25 ) ) PUNCT iajs-2566 295 26 ≀ ≀ NOUN iajs-2566 295 27 𝑝 𝑝 PROPN iajs-2566 295 28 ( ( PUNCT iajs-2566 295 29 𝛼 𝛼 PROPN iajs-2566 295 30 , , PUNCT iajs-2566 295 31 𝛽 𝛽 NOUN iajs-2566 295 32 ) ) PUNCT iajs-2566 295 33 + + X iajs-2566 295 34 𝑝 𝑝 NOUN iajs-2566 295 35 ( ( PUNCT iajs-2566 295 36 𝛽 𝛽 NOUN iajs-2566 295 37 , , PUNCT iajs-2566 295 38 𝛾 𝛾 PROPN iajs-2566 295 39 ) ) PUNCT iajs-2566 296 1 + + X iajs-2566 296 2 𝑝 𝑝 NOUN iajs-2566 296 3 ( ( PUNCT iajs-2566 296 4 𝛼 𝛼 INTJ iajs-2566 296 5 , , PUNCT iajs-2566 296 6 𝛾 𝛾 NOUN iajs-2566 296 7 ) ) PUNCT iajs-2566 296 8 – – PUNCT iajs-2566 296 9 𝑝 𝑝 NOUN iajs-2566 296 10 ( ( PUNCT iajs-2566 296 11 𝛼 𝛼 PROPN iajs-2566 296 12 , , PUNCT iajs-2566 296 13 𝛼 𝛼 NOUN iajs-2566 296 14 ) ) PUNCT iajs-2566 296 15 – – PUNCT iajs-2566 296 16 𝑝 𝑝 NOUN iajs-2566 296 17 ( ( PUNCT iajs-2566 296 18 𝛽 𝛽 PROPN iajs-2566 296 19 , , PUNCT iajs-2566 296 20 𝛽 𝛽 PROPN iajs-2566 296 21 ) ) PUNCT iajs-2566 296 22 – – PUNCT iajs-2566 296 23 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 296 24 , , PUNCT iajs-2566 296 25 𝛾 𝛾 PROPN iajs-2566 296 26 ) ) PUNCT iajs-2566 296 27 + + CCONJ iajs-2566 296 28 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 296 29 , , PUNCT iajs-2566 296 30 𝛾 𝛾 PROPN iajs-2566 296 31 ) ) PUNCT iajs-2566 296 32 – – PUNCT iajs-2566 296 33 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 296 34 , , PUNCT iajs-2566 296 35 𝛾 𝛾 PROPN iajs-2566 296 36 ) ) PUNCT iajs-2566 297 1 + + X iajs-2566 297 2 𝑝 𝑝 NOUN iajs-2566 297 3 ( ( PUNCT iajs-2566 297 4 𝛼 𝛼 INTJ iajs-2566 297 5 , , PUNCT iajs-2566 297 6 πœ‡ πœ‡ ADP iajs-2566 297 7 ) ) PUNCT iajs-2566 297 8 – – PUNCT iajs-2566 297 9 𝑝 𝑝 NOUN iajs-2566 297 10 ( ( PUNCT iajs-2566 297 11 𝛼 𝛼 INTJ iajs-2566 297 12 , , PUNCT iajs-2566 297 13 𝛼 𝛼 PROPN iajs-2566 297 14 ) ) PUNCT iajs-2566 297 15 + + X iajs-2566 297 16 𝑝 𝑝 NOUN iajs-2566 297 17 ( ( PUNCT iajs-2566 297 18 𝛽 𝛽 NOUN iajs-2566 297 19 , , PUNCT iajs-2566 297 20 πœ‡ πœ‡ ADP iajs-2566 297 21 ) ) PUNCT iajs-2566 297 22 – – PUNCT iajs-2566 297 23 𝑝 𝑝 NOUN iajs-2566 297 24 ( ( PUNCT iajs-2566 297 25 𝛽 𝛽 PROPN iajs-2566 297 26 , , PUNCT iajs-2566 297 27 𝛽 𝛽 PROPN iajs-2566 297 28 ) ) PUNCT iajs-2566 297 29 + + CCONJ iajs-2566 297 30 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 297 31 , , PUNCT iajs-2566 297 32 𝛽 𝛽 NOUN iajs-2566 297 33 ) ) PUNCT iajs-2566 297 34 – – PUNCT iajs-2566 297 35 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 297 36 , , PUNCT iajs-2566 297 37 πœ‡ πœ‡ ADP iajs-2566 297 38 ) ) PUNCT iajs-2566 298 1 + + CCONJ iajs-2566 298 2 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 298 3 , , PUNCT iajs-2566 298 4 𝛾 𝛾 PROPN iajs-2566 298 5 ) ) PUNCT iajs-2566 298 6 – – PUNCT iajs-2566 298 7 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 298 8 , , PUNCT iajs-2566 298 9 πœ‡ πœ‡ ADP iajs-2566 298 10 ) ) PUNCT iajs-2566 298 11 + + X iajs-2566 298 12 𝑝 𝑝 NOUN iajs-2566 298 13 ( ( PUNCT iajs-2566 298 14 𝛼 𝛼 INTJ iajs-2566 298 15 , , PUNCT iajs-2566 298 16 πœ‡ πœ‡ ADP iajs-2566 298 17 ) ) PUNCT iajs-2566 298 18 – – PUNCT iajs-2566 298 19 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 298 20 , , PUNCT iajs-2566 298 21 πœ‡ πœ‡ X iajs-2566 298 22 ) ) PUNCT iajs-2566 298 23 . . PUNCT iajs-2566 299 1 β‡’ β‡’ PROPN iajs-2566 299 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 299 3 ( ( PUNCT iajs-2566 299 4 𝛼 𝛼 INTJ iajs-2566 299 5 , , PUNCT iajs-2566 299 6 𝛽 𝛽 PROPN iajs-2566 299 7 , , PUNCT iajs-2566 299 8 𝛾 𝛾 NOUN iajs-2566 299 9 ) ) PUNCT iajs-2566 299 10 ≀ ≀ NOUN iajs-2566 299 11 [ [ PUNCT iajs-2566 299 12 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 299 13 , , PUNCT iajs-2566 299 14 𝛽 𝛽 PROPN iajs-2566 299 15 ) ) PUNCT iajs-2566 300 1 + + CCONJ iajs-2566 300 2 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 300 3 , , PUNCT iajs-2566 300 4 𝛾 𝛾 PROPN iajs-2566 300 5 ) ) PUNCT iajs-2566 300 6 + + CCONJ iajs-2566 300 7 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 300 8 , , PUNCT iajs-2566 300 9 𝛽 𝛽 NOUN iajs-2566 300 10 ) ) PUNCT iajs-2566 300 11 – – PUNCT iajs-2566 300 12 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 300 13 , , PUNCT iajs-2566 300 14 πœ‡ πœ‡ ADP iajs-2566 300 15 ) ) PUNCT iajs-2566 300 16 – – PUNCT iajs-2566 300 17 𝑝 𝑝 NOUN iajs-2566 300 18 ( ( PUNCT iajs-2566 300 19 𝛽 𝛽 PROPN iajs-2566 300 20 , , PUNCT iajs-2566 300 21 𝛽 𝛽 PROPN iajs-2566 300 22 ) ) PUNCT iajs-2566 300 23 – – PUNCT iajs-2566 300 24 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 300 25 , , PUNCT iajs-2566 300 26 𝛾 𝛾 NOUN iajs-2566 300 27 ) ) PUNCT iajs-2566 300 28 ] ] PUNCT iajs-2566 301 1 + + CCONJ iajs-2566 301 2 [ [ PUNCT iajs-2566 301 3 𝑝 𝑝 NOUN iajs-2566 301 4 ( ( PUNCT iajs-2566 301 5 𝛼 𝛼 NOUN iajs-2566 301 6 , , PUNCT iajs-2566 301 7 πœ‡ πœ‡ ADP iajs-2566 301 8 ) ) PUNCT iajs-2566 301 9 + + X iajs-2566 301 10 𝑝 𝑝 NOUN iajs-2566 301 11 ( ( PUNCT iajs-2566 301 12 𝛼 𝛼 INTJ iajs-2566 301 13 , , PUNCT iajs-2566 301 14 𝛾 𝛾 NOUN iajs-2566 301 15 ) ) PUNCT iajs-2566 302 1 + + CCONJ iajs-2566 302 2 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 302 3 , , PUNCT iajs-2566 302 4 𝛾 𝛾 PROPN iajs-2566 302 5 ) ) PUNCT iajs-2566 302 6 – – PUNCT iajs-2566 302 7 𝑝 𝑝 NOUN iajs-2566 302 8 ( ( PUNCT iajs-2566 302 9 𝛼 𝛼 PROPN iajs-2566 302 10 , , PUNCT iajs-2566 302 11 𝛼 𝛼 NOUN iajs-2566 302 12 ) ) PUNCT iajs-2566 302 13 – – PUNCT iajs-2566 302 14 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 302 15 , , PUNCT iajs-2566 302 16 πœ‡ πœ‡ ADP iajs-2566 302 17 ) ) PUNCT iajs-2566 302 18 – – PUNCT iajs-2566 302 19 𝑝(𝛾 𝑝(𝛾 PROPN iajs-2566 302 20 , , PUNCT iajs-2566 302 21 𝛾 𝛾 NOUN iajs-2566 302 22 ) ) PUNCT iajs-2566 302 23 ] ] PUNCT iajs-2566 303 1 + + CCONJ iajs-2566 303 2 [ [ PUNCT iajs-2566 303 3 𝑝 𝑝 NOUN iajs-2566 303 4 ( ( PUNCT iajs-2566 303 5 𝛼 𝛼 NOUN iajs-2566 303 6 , , PUNCT iajs-2566 303 7 𝛽 𝛽 NOUN iajs-2566 303 8 ) ) PUNCT iajs-2566 304 1 + + X iajs-2566 304 2 𝑝 𝑝 NOUN iajs-2566 304 3 ( ( PUNCT iajs-2566 304 4 𝛼 𝛼 INTJ iajs-2566 304 5 , , PUNCT iajs-2566 304 6 πœ‡ πœ‡ ADP iajs-2566 304 7 ) ) PUNCT iajs-2566 304 8 + + X iajs-2566 304 9 𝑝 𝑝 NOUN iajs-2566 304 10 ( ( PUNCT iajs-2566 304 11 𝛽 𝛽 NOUN iajs-2566 304 12 , , PUNCT iajs-2566 304 13 πœ‡ πœ‡ ADP iajs-2566 304 14 ) ) PUNCT iajs-2566 304 15 – – PUNCT iajs-2566 304 16 𝑝 𝑝 NOUN iajs-2566 304 17 ( ( PUNCT iajs-2566 304 18 𝛼 𝛼 PROPN iajs-2566 304 19 , , PUNCT iajs-2566 304 20 𝛼 𝛼 NOUN iajs-2566 304 21 ) ) PUNCT iajs-2566 304 22 – – PUNCT iajs-2566 304 23 𝑝 𝑝 NOUN iajs-2566 304 24 ( ( PUNCT iajs-2566 304 25 𝛽 𝛽 PROPN iajs-2566 304 26 , , PUNCT iajs-2566 304 27 𝛽 𝛽 PROPN iajs-2566 304 28 ) ) PUNCT iajs-2566 304 29 – – PUNCT iajs-2566 304 30 𝑝(πœ‡ 𝑝(πœ‡ PROPN iajs-2566 304 31 , , PUNCT iajs-2566 304 32 πœ‡ πœ‡ ADP iajs-2566 304 33 ) ) PUNCT iajs-2566 304 34 ] ] PUNCT iajs-2566 304 35 𝐷𝑝(𝛼 𝐷𝑝(𝛼 NOUN iajs-2566 304 36 , , PUNCT iajs-2566 304 37 𝛽 𝛽 PROPN iajs-2566 304 38 , , PUNCT iajs-2566 304 39 𝛾 𝛾 NOUN iajs-2566 304 40 ) ) PUNCT iajs-2566 304 41 ≀ ≀ NOUN iajs-2566 304 42 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ VERB iajs-2566 304 43 , , PUNCT iajs-2566 304 44 𝛽 𝛽 NOUN iajs-2566 304 45 , , PUNCT iajs-2566 304 46 𝛾 𝛾 NOUN iajs-2566 304 47 ) ) PUNCT iajs-2566 304 48 + + PUNCT iajs-2566 305 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 305 2 ( ( PUNCT iajs-2566 305 3 𝛼 𝛼 INTJ iajs-2566 305 4 , , PUNCT iajs-2566 305 5 πœ‡ πœ‡ X iajs-2566 305 6 , , PUNCT iajs-2566 305 7 𝛾 𝛾 PROPN iajs-2566 305 8 ) ) PUNCT iajs-2566 305 9 + + PUNCT iajs-2566 306 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 306 2 ( ( PUNCT iajs-2566 306 3 𝛼 𝛼 INTJ iajs-2566 306 4 , , PUNCT iajs-2566 306 5 𝛽 𝛽 NOUN iajs-2566 306 6 , , PUNCT iajs-2566 306 7 πœ‡ πœ‡ ADP iajs-2566 306 8 ) ) PUNCT iajs-2566 306 9 – – PUNCT iajs-2566 306 10 𝐷𝑝(πœ‡ 𝐷𝑝(πœ‡ PROPN iajs-2566 306 11 , , PUNCT iajs-2566 306 12 πœ‡ πœ‡ X iajs-2566 306 13 , , PUNCT iajs-2566 306 14 πœ‡ πœ‡ NOUN iajs-2566 306 15 ) ) PUNCT iajs-2566 306 16 βŽ• βŽ• VERB iajs-2566 306 17 proposition proposition NOUN iajs-2566 306 18 20 20 NUM iajs-2566 306 19 let let VERB iajs-2566 306 20 ( ( PUNCT iajs-2566 306 21 π‘Œ π‘Œ PROPN iajs-2566 306 22 , , PUNCT iajs-2566 306 23 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 306 24 ) ) PUNCT iajs-2566 306 25 be be VERB iajs-2566 306 26 a a DET iajs-2566 306 27 general general ADJ iajs-2566 306 28 partial partial ADJ iajs-2566 306 29 metric metric ADJ iajs-2566 306 30 space space NOUN iajs-2566 306 31 and and CCONJ iajs-2566 306 32 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 306 33 ( ( PUNCT iajs-2566 306 34 𝛼 𝛼 INTJ iajs-2566 306 35 , , PUNCT iajs-2566 306 36 𝛽 𝛽 PROPN iajs-2566 306 37 , , PUNCT iajs-2566 306 38 𝛽 𝛽 NOUN iajs-2566 306 39 ) ) PUNCT iajs-2566 306 40 ≀ ≀ PUNCT iajs-2566 307 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 307 2 ( ( PUNCT iajs-2566 307 3 𝛼 𝛼 INTJ iajs-2566 307 4 , , PUNCT iajs-2566 307 5 𝛾 𝛾 PROPN iajs-2566 307 6 , , PUNCT iajs-2566 307 7 𝛾 𝛾 NOUN iajs-2566 307 8 ) ) PUNCT iajs-2566 308 1 + + CCONJ iajs-2566 308 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 308 3 , , PUNCT iajs-2566 308 4 𝛽 𝛽 NOUN iajs-2566 308 5 , , PUNCT iajs-2566 308 6 𝛽 𝛽 NOUN iajs-2566 308 7 ) ) PUNCT iajs-2566 308 8 – – PUNCT iajs-2566 308 9 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 308 10 , , PUNCT iajs-2566 308 11 𝛾 𝛾 NOUN iajs-2566 308 12 , , PUNCT iajs-2566 308 13 𝛾 𝛾 NOUN iajs-2566 308 14 ) ) PUNCT iajs-2566 308 15 ( ( PUNCT iajs-2566 308 16 1.4 1.4 NUM iajs-2566 308 17 ) ) PUNCT iajs-2566 308 18 holds hold VERB iajs-2566 308 19 then then ADV iajs-2566 308 20 the the DET iajs-2566 308 21 function function NOUN iajs-2566 308 22 𝑝 𝑝 NOUN iajs-2566 308 23 : : PUNCT iajs-2566 308 24 π‘Œ2 π‘Œ2 NOUN iajs-2566 308 25 β†’ β†’ PUNCT iajs-2566 309 1 [ [ X iajs-2566 309 2 0 0 NUM iajs-2566 309 3 , , PUNCT iajs-2566 309 4 ∞ ∞ PROPN iajs-2566 309 5 ) ) PUNCT iajs-2566 309 6 which which PRON iajs-2566 309 7 is be AUX iajs-2566 309 8 defied defy VERB iajs-2566 309 9 by by ADP iajs-2566 309 10 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 309 11 , , PUNCT iajs-2566 309 12 𝛽 𝛽 NOUN iajs-2566 309 13 ) ) PUNCT iajs-2566 310 1 = = SYM iajs-2566 310 2 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 310 3 ( ( PUNCT iajs-2566 310 4 𝛼 𝛼 INTJ iajs-2566 310 5 , , PUNCT iajs-2566 310 6 𝛽 𝛽 PROPN iajs-2566 310 7 , , PUNCT iajs-2566 310 8 𝛽 𝛽 PROPN iajs-2566 310 9 ) ) PUNCT iajs-2566 310 10 is be AUX iajs-2566 310 11 a a DET iajs-2566 310 12 partial partial ADJ iajs-2566 310 13 metric metric NOUN iajs-2566 310 14 on on ADP iajs-2566 310 15 y y PROPN iajs-2566 310 16 . . PUNCT iajs-2566 311 1 proof proof NOUN iajs-2566 311 2 59 59 NUM iajs-2566 311 3 ibn ibn PROPN iajs-2566 311 4 al al PROPN iajs-2566 311 5 - - PUNCT iajs-2566 311 6 haitham haitham PROPN iajs-2566 311 7 jour jour X iajs-2566 311 8 . . PROPN iajs-2566 312 1 for for ADP iajs-2566 312 2 pure pure ADJ iajs-2566 312 3 & & CCONJ iajs-2566 312 4 appl appl PROPN iajs-2566 312 5 . . PUNCT iajs-2566 313 1 sci sci PROPN iajs-2566 313 2 . . PROPN iajs-2566 314 1 34 34 NUM iajs-2566 314 2 ( ( PUNCT iajs-2566 314 3 1 1 NUM iajs-2566 314 4 ) ) PUNCT iajs-2566 314 5 2021 2021 NUM iajs-2566 314 6 1)𝑠𝑖𝑛𝑐𝑒 1)𝑠𝑖𝑛𝑐𝑒 NUM iajs-2566 314 7 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 314 8 , , PUNCT iajs-2566 314 9 𝛽 𝛽 NOUN iajs-2566 314 10 ) ) PUNCT iajs-2566 314 11 = = SYM iajs-2566 314 12 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 314 13 , , PUNCT iajs-2566 314 14 𝛼 𝛼 NOUN iajs-2566 314 15 ) ) PUNCT iajs-2566 314 16 = = SYM iajs-2566 314 17 𝑝(𝛽 𝑝(𝛽 NOUN iajs-2566 314 18 , , PUNCT iajs-2566 314 19 𝛽 𝛽 NOUN iajs-2566 314 20 ) ) PUNCT iajs-2566 314 21 ⇔ ⇔ PROPN iajs-2566 314 22 𝐷𝑝(𝛼 𝐷𝑝(𝛼 PROPN iajs-2566 314 23 , , PUNCT iajs-2566 314 24 𝛽 𝛽 PROPN iajs-2566 314 25 , , PUNCT iajs-2566 314 26 𝛽 𝛽 NOUN iajs-2566 314 27 ) ) PUNCT iajs-2566 314 28 = = PUNCT iajs-2566 315 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADJ iajs-2566 315 2 , , PUNCT iajs-2566 315 3 𝛼 𝛼 X iajs-2566 315 4 , , PUNCT iajs-2566 315 5 𝛼 𝛼 NOUN iajs-2566 315 6 ) ) PUNCT iajs-2566 315 7 = = SYM iajs-2566 315 8 𝐷𝑝(𝛽 𝐷𝑝(𝛽 NOUN iajs-2566 315 9 , , PUNCT iajs-2566 315 10 𝛽 𝛽 NOUN iajs-2566 315 11 , , PUNCT iajs-2566 315 12 𝛽 𝛽 NOUN iajs-2566 315 13 ) ) PUNCT iajs-2566 315 14 ⇔ ⇔ X iajs-2566 315 15 𝛼 𝛼 NOUN iajs-2566 315 16 = = NOUN iajs-2566 315 17 𝛽. 𝛽. NOUN iajs-2566 315 18 2 2 NUM iajs-2566 315 19 ) ) PUNCT iajs-2566 315 20 𝑠𝑖𝑛𝑐𝑒 𝑠𝑖𝑛𝑐𝑒 PROPN iajs-2566 316 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 316 2 ( ( PUNCT iajs-2566 316 3 𝛼 𝛼 INTJ iajs-2566 316 4 , , PUNCT iajs-2566 316 5 𝛼 𝛼 X iajs-2566 316 6 , , PUNCT iajs-2566 316 7 𝛼 𝛼 NOUN iajs-2566 316 8 ) ) PUNCT iajs-2566 316 9 ≀ ≀ PUNCT iajs-2566 317 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 317 2 ( ( PUNCT iajs-2566 317 3 𝛼 𝛼 PROPN iajs-2566 317 4 , , PUNCT iajs-2566 317 5 𝛽 𝛽 NOUN iajs-2566 317 6 , , PUNCT iajs-2566 317 7 𝛽 𝛽 NOUN iajs-2566 317 8 ) ) PUNCT iajs-2566 317 9 π‘‘β„Žπ‘’π‘› π‘‘β„Žπ‘’π‘› VERB iajs-2566 317 10 𝑝 𝑝 PROPN iajs-2566 317 11 ( ( PUNCT iajs-2566 317 12 𝛼 𝛼 PROPN iajs-2566 317 13 , , PUNCT iajs-2566 317 14 𝛼 𝛼 NOUN iajs-2566 317 15 ) ) PUNCT iajs-2566 317 16 ≀ ≀ NOUN iajs-2566 317 17 𝑝 𝑝 PROPN iajs-2566 317 18 ( ( PUNCT iajs-2566 317 19 𝛼 𝛼 INTJ iajs-2566 317 20 , , PUNCT iajs-2566 317 21 𝛽 𝛽 NOUN iajs-2566 317 22 ) ) PUNCT iajs-2566 317 23 βˆ€ βˆ€ PUNCT iajs-2566 318 1 𝛼 𝛼 NOUN iajs-2566 318 2 , , PUNCT iajs-2566 318 3 𝛽 𝛽 PROPN iajs-2566 318 4 ∈ ∈ PROPN iajs-2566 318 5 𝛼 𝛼 NOUN iajs-2566 318 6 3 3 NUM iajs-2566 318 7 ) ) PUNCT iajs-2566 318 8 trivial trivial ADJ iajs-2566 318 9 4 4 NUM iajs-2566 318 10 ) ) PUNCT iajs-2566 318 11 𝑝(𝛼 𝑝(𝛼 PROPN iajs-2566 318 12 , , PUNCT iajs-2566 318 13 𝛽 𝛽 NOUN iajs-2566 318 14 ) ) PUNCT iajs-2566 318 15 = = SYM iajs-2566 319 1 𝐷𝑝 𝐷𝑝 PROPN iajs-2566 319 2 ( ( PUNCT iajs-2566 319 3 𝛼 𝛼 INTJ iajs-2566 319 4 , , PUNCT iajs-2566 319 5 𝛽 𝛽 PROPN iajs-2566 319 6 , , PUNCT iajs-2566 319 7 𝛽 𝛽 NOUN iajs-2566 319 8 ) ) PUNCT iajs-2566 319 9 ≀ ≀ PUNCT iajs-2566 320 1 𝐷𝑝(𝛼 𝐷𝑝(𝛼 ADV iajs-2566 320 2 , , PUNCT iajs-2566 320 3 𝛾 𝛾 X iajs-2566 320 4 , , PUNCT iajs-2566 320 5 𝛾 𝛾 NOUN iajs-2566 320 6 ) ) PUNCT iajs-2566 321 1 + + CCONJ iajs-2566 321 2 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 321 3 , , PUNCT iajs-2566 321 4 𝛽 𝛽 NOUN iajs-2566 321 5 , , PUNCT iajs-2566 321 6 𝛽 𝛽 NOUN iajs-2566 321 7 ) ) PUNCT iajs-2566 321 8 – – PUNCT iajs-2566 321 9 𝐷𝑝(𝛾 𝐷𝑝(𝛾 NOUN iajs-2566 321 10 , , PUNCT iajs-2566 321 11 𝛾 𝛾 NOUN iajs-2566 321 12 , , PUNCT iajs-2566 321 13 𝛾 𝛾 NOUN iajs-2566 321 14 ) ) PUNCT iajs-2566 321 15 π‘“π‘Ÿπ‘œπ‘š π‘“π‘Ÿπ‘œπ‘š PROPN iajs-2566 321 16 ( ( PUNCT iajs-2566 321 17 1.3 1.3 NUM iajs-2566 321 18 ) ) PUNCT iajs-2566 321 19 = = SYM iajs-2566 321 20 𝑝 𝑝 PROPN iajs-2566 321 21 ( ( PUNCT iajs-2566 321 22 𝛼 𝛼 NOUN iajs-2566 321 23 , , PUNCT iajs-2566 321 24 𝛾 𝛾 NOUN iajs-2566 321 25 ) ) PUNCT iajs-2566 322 1 + + CCONJ iajs-2566 322 2 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 322 3 , , PUNCT iajs-2566 322 4 𝛽 𝛽 NOUN iajs-2566 322 5 ) ) PUNCT iajs-2566 322 6 βˆ’ βˆ’ PROPN iajs-2566 322 7 𝑝(𝛾 𝑝(𝛾 NOUN iajs-2566 322 8 , , PUNCT iajs-2566 322 9 𝛾 𝛾 NOUN iajs-2566 322 10 ) ) PUNCT iajs-2566 322 11 . . PUNCT iajs-2566 323 1 βŽ• βŽ• PROPN iajs-2566 324 1 references reference NOUN iajs-2566 324 2 1 1 NUM iajs-2566 324 3 . . PUNCT iajs-2566 325 1 czerwik czerwik PROPN iajs-2566 325 2 , , PUNCT iajs-2566 325 3 stefan stefan PROPN iajs-2566 325 4 . . PUNCT iajs-2566 326 1 contraction contraction NOUN iajs-2566 326 2 mappings mapping NOUN iajs-2566 326 3 in in ADP iajs-2566 326 4 $ $ SYM iajs-2566 326 5 b b PRON iajs-2566 326 6 $ $ SYM iajs-2566 326 7 -metric -metric ADJ iajs-2566 326 8 spaces space NOUN iajs-2566 326 9 , , PUNCT iajs-2566 326 10 acta acta PROPN iajs-2566 326 11 mathematica mathematica PROPN iajs-2566 326 12 et et PROPN iajs-2566 326 13 informatica informatica PROPN iajs-2566 326 14 universitatis universitatis PROPN iajs-2566 326 15 ostraviensis ostraviensis PROPN iajs-2566 326 16 . . PUNCT iajs-2566 327 1 1993 1993 NUM iajs-2566 327 2 , , PUNCT iajs-2566 327 3 1 1 NUM iajs-2566 327 4 , , PUNCT iajs-2566 327 5 1 1 NUM iajs-2566 327 6 , , PUNCT iajs-2566 327 7 5 5 NUM iajs-2566 327 8 - - SYM iajs-2566 327 9 11 11 NUM iajs-2566 327 10 . . NOUN iajs-2566 328 1 2 2 NUM iajs-2566 328 2 . . X iajs-2566 328 3 mustafa mustafa PROPN iajs-2566 328 4 , , PUNCT iajs-2566 328 5 zead zead PROPN iajs-2566 328 6 . . PUNCT iajs-2566 328 7 ; ; PUNCT iajs-2566 328 8 obiedat obiedat NOUN iajs-2566 328 9 , , PUNCT iajs-2566 328 10 hamed hamed PROPN iajs-2566 328 11 . . PUNCT iajs-2566 328 12 ; ; PUNCT iajs-2566 328 13 awawdeh awawdeh NOUN iajs-2566 328 14 , , PUNCT iajs-2566 328 15 fadi fadi NOUN iajs-2566 328 16 . . PUNCT iajs-2566 329 1 some some DET iajs-2566 329 2 fixed fix VERB iajs-2566 329 3 point point NOUN iajs-2566 329 4 theorem theorem NOUN iajs-2566 329 5 for for ADP iajs-2566 329 6 mapping mapping NOUN iajs-2566 329 7 on on ADP iajs-2566 329 8 complete complete ADJ iajs-2566 329 9 g g NOUN iajs-2566 329 10 - - PUNCT iajs-2566 329 11 metric metric ADJ iajs-2566 329 12 spaces space NOUN iajs-2566 329 13 . . PUNCT iajs-2566 330 1 fixed fix VERB iajs-2566 330 2 point point NOUN iajs-2566 330 3 theory theory NOUN iajs-2566 330 4 and and CCONJ iajs-2566 330 5 applications application NOUN iajs-2566 330 6 . . PUNCT iajs-2566 331 1 2008 2008 NUM iajs-2566 331 2 , , PUNCT iajs-2566 331 3 2008 2008 NUM iajs-2566 331 4 , , PUNCT iajs-2566 331 5 1 1 NUM iajs-2566 331 6 , , PUNCT iajs-2566 331 7 189870 189870 NUM iajs-2566 331 8 . . PUNCT iajs-2566 332 1 3.gahler 3.gahler NUM iajs-2566 332 2 , , PUNCT iajs-2566 332 3 siegfried siegfrie VERB iajs-2566 332 4 . . PUNCT iajs-2566 333 1 2‐metrische 2‐metrische PROPN iajs-2566 333 2 rΓ€ume rΓ€ume PROPN iajs-2566 333 3 und und VERB iajs-2566 333 4 ihre ihre NOUN iajs-2566 333 5 topologische topologische NOUN iajs-2566 333 6 struktur struktur PROPN iajs-2566 333 7 , , PUNCT iajs-2566 333 8 mathematische mathematische NOUN iajs-2566 333 9 nachrichten nachrichten NOUN iajs-2566 333 10 , , PUNCT iajs-2566 333 11 1963 1963 NUM iajs-2566 333 12 , , PUNCT iajs-2566 333 13 26,1‐4 26,1‐4 NUM iajs-2566 333 14 , , PUNCT iajs-2566 333 15 115 115 NUM iajs-2566 333 16 - - SYM iajs-2566 333 17 148 148 NUM iajs-2566 333 18 . . PUNCT iajs-2566 334 1 6.sedghi 6.sedghi NUM iajs-2566 334 2 , , PUNCT iajs-2566 334 3 shaban shaban PROPN iajs-2566 334 4 . . PROPN iajs-2566 334 5 ; ; PUNCT iajs-2566 334 6 shobe shobe PROPN iajs-2566 334 7 , , PUNCT iajs-2566 334 8 nabi nabi PROPN iajs-2566 334 9 . . PUNCT iajs-2566 334 10 ; ; PUNCT iajs-2566 335 1 zhou zhou PROPN iajs-2566 335 2 , , PUNCT iajs-2566 335 3 haiyun haiyun NOUN iajs-2566 335 4 . . PUNCT iajs-2566 336 1 a a DET iajs-2566 336 2 common common ADJ iajs-2566 336 3 fixed fix VERB iajs-2566 336 4 point point NOUN iajs-2566 336 5 theorem theorem VERB iajs-2566 336 6 in in ADP iajs-2566 336 7 - - PUNCT iajs-2566 336 8 metric metric ADJ iajs-2566 336 9 spaces space NOUN iajs-2566 336 10 , , PUNCT iajs-2566 336 11 fixed fix VERB iajs-2566 336 12 point point NOUN iajs-2566 336 13 theory theory NOUN iajs-2566 336 14 and and CCONJ iajs-2566 336 15 applications application NOUN iajs-2566 336 16 , , PUNCT iajs-2566 336 17 2007 2007 NUM iajs-2566 336 18 , , PUNCT iajs-2566 336 19 2007 2007 NUM iajs-2566 336 20 , , PUNCT iajs-2566 336 21 1 1 NUM iajs-2566 336 22 , , PUNCT iajs-2566 336 23 027906 027906 NUM iajs-2566 336 24 . . PUNCT iajs-2566 337 1 5 5 NUM iajs-2566 337 2 . . PUNCT iajs-2566 337 3 matthews matthews PROPN iajs-2566 337 4 , , PUNCT iajs-2566 337 5 steve steve PROPN iajs-2566 337 6 g. g. PROPN iajs-2566 337 7 partial partial ADJ iajs-2566 337 8 metric metric ADJ iajs-2566 337 9 topology topology NOUN iajs-2566 337 10 , , PUNCT iajs-2566 337 11 annals annal NOUN iajs-2566 337 12 of of ADP iajs-2566 337 13 the the DET iajs-2566 337 14 new new PROPN iajs-2566 337 15 york york PROPN iajs-2566 337 16 academy academy PROPN iajs-2566 337 17 of of ADP iajs-2566 337 18 sciencespaper sciencespaper PROPN iajs-2566 337 19 edition edition PROPN iajs-2566 337 20 . . PUNCT iajs-2566 337 21 1994 1994 NUM iajs-2566 337 22 , , PUNCT iajs-2566 337 23 728 728 NUM iajs-2566 337 24 , , PUNCT iajs-2566 337 25 183 183 NUM iajs-2566 337 26 - - SYM iajs-2566 337 27 197 197 NUM iajs-2566 337 28 . . NOUN iajs-2566 338 1 6 6 NUM iajs-2566 338 2 . . NUM iajs-2566 338 3 aydi aydi VERB iajs-2566 338 4 , , PUNCT iajs-2566 338 5 hassen hassen NOUN iajs-2566 338 6 , , PUNCT iajs-2566 338 7 et et PROPN iajs-2566 338 8 al al PROPN iajs-2566 338 9 . . PROPN iajs-2566 339 1 on on ADP iajs-2566 339 2 Ο† Ο† NUM iajs-2566 339 3 - - PUNCT iajs-2566 339 4 contraction contraction NOUN iajs-2566 339 5 type type NOUN iajs-2566 339 6 couplings coupling NOUN iajs-2566 339 7 in in ADP iajs-2566 339 8 partial partial ADJ iajs-2566 339 9 metric metric ADJ iajs-2566 339 10 spaces space NOUN iajs-2566 339 11 , , PUNCT iajs-2566 339 12 journal journal NOUN iajs-2566 339 13 of of ADP iajs-2566 339 14 mathematical mathematical ADJ iajs-2566 339 15 analysis analysis NOUN iajs-2566 339 16 . . PUNCT iajs-2566 340 1 2017 2017 NUM iajs-2566 340 2 , , PUNCT iajs-2566 340 3 8 8 NUM iajs-2566 340 4 , , PUNCT iajs-2566 340 5 4 4 NUM iajs-2566 340 6 , , PUNCT iajs-2566 340 7 78 78 NUM iajs-2566 340 8 - - SYM iajs-2566 340 9 89 89 NUM iajs-2566 340 10 . . PUNCT iajs-2566 341 1 7 7 NUM iajs-2566 341 2 . . X iajs-2566 341 3 şahin şahin PROPN iajs-2566 341 4 , , PUNCT iajs-2566 341 5 memet memet PROPN iajs-2566 341 6 . . PUNCT iajs-2566 341 7 ; ; PUNCT iajs-2566 342 1 kargin kargin PROPN iajs-2566 342 2 , , PUNCT iajs-2566 342 3 abdullah abdullah PROPN iajs-2566 342 4 . . PUNCT iajs-2566 342 5 ; ; PUNCT iajs-2566 342 6 Γ§oban Γ§oban PROPN iajs-2566 342 7 , , PUNCT iajs-2566 342 8 mehmet mehmet PROPN iajs-2566 342 9 ali ali PROPN iajs-2566 342 10 . . PUNCT iajs-2566 343 1 fixed fix VERB iajs-2566 343 2 point point NOUN iajs-2566 343 3 theorem theorem NOUN iajs-2566 343 4 for for ADP iajs-2566 343 5 neutrosophic neutrosophic ADJ iajs-2566 343 6 triplet triplet NOUN iajs-2566 343 7 partial partial ADJ iajs-2566 343 8 metric metric ADJ iajs-2566 343 9 space space NOUN iajs-2566 343 10 , , PUNCT iajs-2566 343 11 symmetry symmetry NOUN iajs-2566 343 12 . . PUNCT iajs-2566 344 1 2018 2018 NUM iajs-2566 344 2 , , PUNCT iajs-2566 344 3 10 10 NUM iajs-2566 344 4 , , PUNCT iajs-2566 344 5 7 7 NUM iajs-2566 344 6 , , PUNCT iajs-2566 344 7 240 240 NUM iajs-2566 344 8 . . NOUN iajs-2566 344 9 8 8 NUM iajs-2566 344 10 . . X iajs-2566 344 11 pant pant NOUN iajs-2566 344 12 , , PUNCT iajs-2566 344 13 rajendra rajendra PROPN iajs-2566 344 14 , , PUNCT iajs-2566 344 15 et et PROPN iajs-2566 344 16 al al PROPN iajs-2566 344 17 . . PUNCT iajs-2566 345 1 some some DET iajs-2566 345 2 new new ADJ iajs-2566 345 3 fixed fix VERB iajs-2566 345 4 point point NOUN iajs-2566 345 5 theorems theorem NOUN iajs-2566 345 6 in in ADP iajs-2566 345 7 partial partial ADJ iajs-2566 345 8 metric metric ADJ iajs-2566 345 9 spaces space NOUN iajs-2566 345 10 with with ADP iajs-2566 345 11 applications application NOUN iajs-2566 345 12 , , PUNCT iajs-2566 345 13 journal journal NOUN iajs-2566 345 14 of of ADP iajs-2566 345 15 function function NOUN iajs-2566 345 16 spaces space NOUN iajs-2566 345 17 . . PUNCT iajs-2566 346 1 2017 2017 NUM iajs-2566 346 2 , , PUNCT iajs-2566 346 3 2017 2017 NUM iajs-2566 346 4 . . PUNCT iajs-2566 347 1 9 9 X iajs-2566 347 2 . . X iajs-2566 347 3 altun altun NOUN iajs-2566 347 4 , , PUNCT iajs-2566 347 5 ishak ishak PROPN iajs-2566 347 6 . . PUNCT iajs-2566 347 7 ; ; PUNCT iajs-2566 348 1 erduran erduran VERB iajs-2566 348 2 , , PUNCT iajs-2566 348 3 ali ali PROPN iajs-2566 348 4 . . PROPN iajs-2566 349 1 fixed fix VERB iajs-2566 349 2 point point NOUN iajs-2566 349 3 theorems theorem NOUN iajs-2566 349 4 for for ADP iajs-2566 349 5 monotone monotone ADJ iajs-2566 349 6 mappings mapping NOUN iajs-2566 349 7 on on ADP iajs-2566 349 8 partial partial ADJ iajs-2566 349 9 metric metric ADJ iajs-2566 349 10 spaces space NOUN iajs-2566 349 11 , , PUNCT iajs-2566 349 12 fixed fix VERB iajs-2566 349 13 point point NOUN iajs-2566 349 14 theory theory NOUN iajs-2566 349 15 and and CCONJ iajs-2566 349 16 applications application NOUN iajs-2566 349 17 . . PUNCT iajs-2566 350 1 2011 2011 NUM iajs-2566 350 2 , , PUNCT iajs-2566 350 3 2011,1 2011,1 NUM iajs-2566 350 4 , , PUNCT iajs-2566 350 5 508730 508730 NUM iajs-2566 350 6 . . PUNCT iajs-2566 351 1 10 10 NUM iajs-2566 351 2 . . PUNCT iajs-2566 351 3 karapinar karapinar PROPN iajs-2566 351 4 , , PUNCT iajs-2566 351 5 erdal erdal PROPN iajs-2566 351 6 . . 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PROPN iajs-2566 355 10 cuza cuza PROPN iajs-2566 355 11 din din PROPN iajs-2566 355 12 lasi lasi PROPN iajs-2566 355 13 . . PUNCT iajs-2566 356 1 serie serie PROPN iajs-2566 356 2 noua noua PROPN iajs-2566 356 3 mathematica mathematica PROPN iajs-2566 356 4 . . PROPN iajs-2566 357 1 2000 2000 NUM iajs-2566 357 2 , , PUNCT iajs-2566 357 3 46,3 46,3 NUM iajs-2566 357 4 , , PUNCT iajs-2566 357 5 24 24 NUM iajs-2566 357 6 . . NOUN iajs-2566 357 7 12 12 NUM iajs-2566 357 8 . . PUNCT iajs-2566 358 1 fora fora PROPN iajs-2566 358 2 , , PUNCT iajs-2566 358 3 ali ali PROPN iajs-2566 358 4 ahmad ahmad PROPN iajs-2566 358 5 . . PUNCT iajs-2566 358 6 ; ; PUNCT iajs-2566 359 1 massadeh massadeh PROPN iajs-2566 359 2 , , PUNCT iajs-2566 359 3 mourad mourad PROPN iajs-2566 359 4 oqla oqla PROPN iajs-2566 359 5 . . 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PROPN iajs-2566 362 10 on on ADP iajs-2566 362 11 d d ADJ iajs-2566 362 12 - - ADJ iajs-2566 362 13 metric metric ADJ iajs-2566 362 14 spaces space NOUN iajs-2566 362 15 , , PUNCT iajs-2566 362 16 journal journal NOUN iajs-2566 362 17 of of ADP iajs-2566 362 18 global global ADJ iajs-2566 362 19 research research NOUN iajs-2566 362 20 in in ADP iajs-2566 362 21 mathematical mathematical ADJ iajs-2566 362 22 archives archive NOUN iajs-2566 362 23 . . PUNCT iajs-2566 363 1 2013 2013 NUM iajs-2566 363 2 , , PUNCT iajs-2566 363 3 1,12 1,12 NUM iajs-2566 363 4 . . PUNCT