id sid tid token lemma pos iajs-1988 1 1 microsoft microsoft PROPN iajs-1988 1 2 word word NOUN iajs-1988 1 3 157 157 NUM iajs-1988 1 4 - - SYM iajs-1988 1 5 166 166 NUM iajs-1988 1 6             SPACE iajs-1988 1 7 157 157 NUM iajs-1988 1 8     SPACE iajs-1988 1 9 ibn ibn PROPN iajs-1988 1 10 al al PROPN iajs-1988 1 11 - - PUNCT iajs-1988 1 12 haitham haitham PROPN iajs-1988 1 13 jour jour X iajs-1988 1 14 . . PROPN iajs-1988 2 1 for for ADP iajs-1988 2 2 pure pure ADJ iajs-1988 2 3 & & CCONJ iajs-1988 2 4 appl.sci appl.sci PROPN iajs-1988 2 5 . . PUNCT iajs-1988 3 1 ihjpas ihjpas PROPN iajs-1988 3 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 3 3 vol vol NOUN iajs-1988 3 4 . . PUNCT iajs-1988 4 1 32 32 NUM iajs-1988 4 2 ( ( PUNCT iajs-1988 4 3 1 1 NUM iajs-1988 4 4 ) ) PUNCT iajs-1988 4 5 2019 2019 NUM iajs-1988 4 6 contractiveimappings contractiveimapping NOUN iajs-1988 4 7 having have VERB iajs-1988 4 8 mixed mix VERB iajs-1988 4 9 finite finite ADJ iajs-1988 4 10 monotoneiproperty monotoneiproperty NOUN iajs-1988 4 11 in in ADP iajs-1988 4 12 generalizedimetric generalizedimetric ADJ iajs-1988 4 13 spaces space NOUN iajs-1988 4 14 zena zena PROPN iajs-1988 4 15 hussein hussein PROPN iajs-1988 4 16 maibed maibe VERB iajs-1988 4 17 mrs mrs PROPN iajs-1988 4 18 _ _ PROPN iajs-1988 4 19 zena.hussein@yahoo.com zena.hussein@yahoo.com PROPN iajs-1988 4 20 department department PROPN iajs-1988 4 21 of of ADP iajs-1988 4 22 mathematics mathematics PROPN iajs-1988 4 23 , , PUNCT iajs-1988 4 24 college college NOUN iajs-1988 4 25 of of ADP iajs-1988 4 26 education education NOUN iajs-1988 4 27 for for ADP iajs-1988 4 28 pure pure ADJ iajs-1988 4 29 science science NOUN iajs-1988 4 30 , , PUNCT iajs-1988 4 31 ibn ibn PROPN iajs-1988 4 32 al al PROPN iajs-1988 4 33 - - PUNCT iajs-1988 4 34 haitham haitham PROPN iajs-1988 4 35 , , PUNCT iajs-1988 4 36 university university PROPN iajs-1988 4 37 of of ADP iajs-1988 4 38 baghdad baghdad PROPN iajs-1988 4 39 , , PUNCT iajs-1988 4 40 baghdad baghdad PROPN iajs-1988 4 41 , , PUNCT iajs-1988 4 42 iraq iraq PROPN iajs-1988 4 43 . . PUNCT iajs-1988 5 1 article article NOUN iajs-1988 5 2 history history NOUN iajs-1988 5 3 : : PUNCT iajs-1988 5 4 received receive VERB iajs-1988 5 5 25 25 NUM iajs-1988 5 6 october october PROPN iajs-1988 5 7 2018 2018 NUM iajs-1988 5 8 , , PUNCT iajs-1988 5 9 accepted accept VERB iajs-1988 5 10 11 11 NUM iajs-1988 5 11 november november PROPN iajs-1988 5 12 2018 2018 NUM iajs-1988 5 13 , , PUNCT iajs-1988 5 14 publish publish VERB iajs-1988 5 15 january january PROPN iajs-1988 5 16 2019 2019 NUM iajs-1988 5 17 abstract abstract ADV iajs-1988 5 18 the the DET iajs-1988 5 19 concepts concept NOUN iajs-1988 5 20 of of ADP iajs-1988 5 21 the the DET iajs-1988 5 22 modified modify VERB iajs-1988 5 23 tuple tuple NOUN iajs-1988 5 24 coincidence coincidence NOUN iajs-1988 5 25 points point NOUN iajs-1988 5 26 and and CCONJ iajs-1988 5 27 the the DET iajs-1988 5 28 mixed mixed ADJ iajs-1988 5 29 finite finite NOUN iajs-1988 5 30 monotone monotone ADJ iajs-1988 5 31 property property NOUN iajs-1988 5 32 is be AUX iajs-1988 5 33 introduced introduce VERB iajs-1988 5 34 in in ADP iajs-1988 5 35 this this DET iajs-1988 5 36 paper paper NOUN iajs-1988 5 37 . . PUNCT iajs-1988 6 1 also also ADV iajs-1988 6 2 , , PUNCT iajs-1988 6 3 the the DET iajs-1988 6 4 existence existence NOUN iajs-1988 6 5 and and CCONJ iajs-1988 6 6 uniqueness uniqueness NOUN iajs-1988 6 7 of of ADP iajs-1988 6 8 modified modify VERB iajs-1988 6 9 tupled tuple VERB iajs-1988 6 10 coincidence coincidence NOUN iajs-1988 6 11 point point NOUN iajs-1988 6 12 is be AUX iajs-1988 6 13 discusses discusse NOUN iajs-1988 6 14 without without ADP iajs-1988 6 15 continuous continuous ADJ iajs-1988 6 16 condition condition NOUN iajs-1988 6 17 for for ADP iajs-1988 6 18 mappings mapping NOUN iajs-1988 6 19 having have VERB iajs-1988 6 20 mixed mixed ADJ iajs-1988 6 21 finite finite ADJ iajs-1988 6 22 monotone monotone ADJ iajs-1988 6 23 property property NOUN iajs-1988 6 24 in in ADP iajs-1988 6 25 generalized generalized ADJ iajs-1988 6 26 metric metric ADJ iajs-1988 6 27 spaces space NOUN iajs-1988 6 28 . . PUNCT iajs-1988 7 1 keywords keyword NOUN iajs-1988 7 2 : : PUNCT iajs-1988 7 3 generalized generalize VERB iajs-1988 7 4 metric metric ADJ iajs-1988 7 5 spaces space NOUN iajs-1988 7 6 , , PUNCT iajs-1988 7 7 fixed fix VERB iajs-1988 7 8 point point NOUN iajs-1988 7 9 , , PUNCT iajs-1988 7 10 coincidence coincidence NOUN iajs-1988 7 11 point point NOUN iajs-1988 7 12 , , PUNCT iajs-1988 7 13 monotone monotone ADJ iajs-1988 7 14 property property NOUN iajs-1988 7 15 . . PUNCT iajs-1988 8 1 1 1 X iajs-1988 8 2 . . X iajs-1988 8 3 introduction introduction NOUN iajs-1988 8 4 in in ADP iajs-1988 8 5 2000,idhage 2000,idhage PROPN iajs-1988 8 6 [ [ X iajs-1988 8 7 1 1 NUM iajs-1988 8 8 ] ] PUNCT iajs-1988 8 9 introduced𝐷–metric introduced𝐷–metric ADJ iajs-1988 8 10 space space NOUN iajs-1988 8 11 as as ADP iajs-1988 8 12 a a DET iajs-1988 8 13 generalization generalization NOUN iajs-1988 8 14 of of ADP iajs-1988 8 15 metric metric ADJ iajs-1988 8 16 space space NOUN iajs-1988 9 1 and and CCONJ iajs-1988 9 2 he he PRON iajs-1988 9 3 proved prove VERB iajs-1988 9 4 many many ADJ iajs-1988 9 5 results result NOUN iajs-1988 9 6 in in ADP iajs-1988 9 7 this this DET iajs-1988 9 8 spaceibut spaceibut NOUN iajs-1988 9 9 in in ADP iajs-1988 9 10 2005 2005 NUM iajs-1988 9 11 , , PUNCT iajs-1988 9 12 mustafa mustafa NOUN iajs-1988 9 13 and and CCONJ iajs-1988 9 14 sims sim NOUN iajs-1988 9 15 [ [ X iajs-1988 9 16 2 2 NUM iajs-1988 9 17 ] ] PUNCT iajs-1988 9 18 proved prove VERB iajs-1988 9 19 thatithe thatithe NOUN iajs-1988 9 20 results result NOUN iajs-1988 9 21 presented present VERB iajs-1988 9 22 by by ADP iajs-1988 9 23 dhage dhage NOUN iajs-1988 9 24 are be AUX iajs-1988 9 25 invalid invalid ADJ iajs-1988 9 26 in in ADP iajs-1988 9 27 topological topological ADJ iajs-1988 9 28 structure structure NOUN iajs-1988 9 29 and and CCONJ iajs-1988 9 30 hence hence ADV iajs-1988 9 31 they they PRON iajs-1988 9 32 introducedi𝐺–metric introducedi𝐺–metric ADJ iajs-1988 9 33 space space NOUN iajs-1988 9 34 and and CCONJ iajs-1988 9 35 as as ADP iajs-1988 9 36 a a DET iajs-1988 9 37 generalized generalized ADJ iajs-1988 9 38 of of ADP iajs-1988 9 39 metric metric ADJ iajs-1988 9 40 space space NOUN iajs-1988 9 41 . . PUNCT iajs-1988 10 1 on on ADP iajs-1988 10 2 other other ADJ iajs-1988 10 3 bhashkar bhashkar NOUN iajs-1988 10 4 andilakshmikantham andilakshmikantham PROPN iajs-1988 10 5 in in ADP iajs-1988 10 6 [ [ X iajs-1988 10 7 3 3 NUM iajs-1988 10 8 ] ] PUNCT iajs-1988 10 9 introduced introduce VERB iajs-1988 10 10 the the DET iajs-1988 10 11 conceptiof conceptiof NOUN iajs-1988 10 12 coupled couple VERB iajs-1988 10 13 fixed fix VERB iajs-1988 10 14 point point NOUN iajs-1988 10 15 and and CCONJ iajs-1988 10 16 proved prove VERB iajs-1988 10 17 the the DET iajs-1988 10 18 existence existence NOUN iajs-1988 10 19 of of ADP iajs-1988 10 20 a a DET iajs-1988 10 21 coupledifixed coupledifixe VERB iajs-1988 10 22 theoremiin theoremiin NOUN iajs-1988 10 23 partiallyiordered partiallyiordere VERB iajs-1988 10 24 complete complete ADJ iajs-1988 10 25 metric metric ADJ iajs-1988 10 26 space space NOUN iajs-1988 10 27 . . PUNCT iajs-1988 11 1 in in ADP iajs-1988 11 2 2009 2009 NUM iajs-1988 11 3 , , PUNCT iajs-1988 11 4 lakshmikantham lakshmikantham ADJ iajs-1988 11 5 and and CCONJ iajs-1988 11 6 ciric ciric ADJ iajs-1988 11 7 [ [ X iajs-1988 11 8 4 4 NUM iajs-1988 11 9 ] ] PUNCT iajs-1988 11 10 definedimixedi𝑔–monotone definedimixedi𝑔–monotone PROPN iajs-1988 11 11 propertyiand propertyiand NOUN iajs-1988 11 12 coupled couple VERB iajs-1988 11 13 coincidenceipoint coincidenceipoint NOUN iajs-1988 11 14 in in ADP iajs-1988 11 15 partiallyiordered partiallyiordere VERB iajs-1988 11 16 metric metric ADJ iajs-1988 11 17 spaces space NOUN iajs-1988 11 18 , , PUNCT iajs-1988 11 19 also also ADV iajs-1988 11 20 in in ADP iajs-1988 11 21 2011 2011 NUM iajs-1988 11 22 , , PUNCT iajs-1988 11 23 berinde berinde NOUN iajs-1988 11 24 and and CCONJ iajs-1988 11 25 borcut borcut VERB iajs-1988 11 26 [ [ PUNCT iajs-1988 11 27 5 5 NUM iajs-1988 11 28 ] ] PUNCT iajs-1988 11 29 introduced introduce VERB iajs-1988 11 30 the the DET iajs-1988 11 31 concept concept NOUN iajs-1988 11 32 ofitriple ofitriple ADP iajs-1988 11 33 fixed fix VERB iajs-1988 11 34 pointiand pointiand NOUN iajs-1988 11 35 proved prove VERB iajs-1988 11 36 some some DET iajs-1988 11 37 resultsia resultsia PROPN iajs-1988 11 38 roundiand roundiand NOUN iajs-1988 11 39 in in ADP iajs-1988 11 40 2012 2012 NUM iajs-1988 11 41 , , PUNCT iajs-1988 11 42 berinde berinde NOUN iajs-1988 11 43 and and CCONJ iajs-1988 11 44 borcut borcut VERB iajs-1988 11 45 [ [ PUNCT iajs-1988 11 46 6 6 NUM iajs-1988 11 47 ] ] PUNCT iajs-1988 11 48 defined define VERB iajs-1988 11 49 the the DET iajs-1988 11 50 concept concept NOUN iajs-1988 11 51 of of ADP iajs-1988 11 52 triple triple ADJ iajs-1988 11 53 coincidenceipoint coincidenceipoint NOUN iajs-1988 11 54 and and CCONJ iajs-1988 11 55 establishedisome establishedisome VERB iajs-1988 11 56 triple triple ADJ iajs-1988 11 57 coincidenceipoint coincidenceipoint NOUN iajs-1988 11 58 theoremsiin theoremsiin NOUN iajs-1988 11 59 partially partially ADV iajs-1988 11 60 orderedimetric orderedimetric ADJ iajs-1988 11 61 space space NOUN iajs-1988 11 62 . . PUNCT iajs-1988 12 1 in in ADP iajs-1988 12 2 this this DET iajs-1988 12 3 paper paper NOUN iajs-1988 12 4 , , PUNCT iajs-1988 12 5 we we PRON iajs-1988 12 6 will will AUX iajs-1988 12 7 give give VERB iajs-1988 12 8 a a DET iajs-1988 12 9 mixed mixed ADJ iajs-1988 12 10 finite finite NOUN iajs-1988 12 11 monotone monotone ADJ iajs-1988 12 12 property property NOUN iajs-1988 12 13 and and CCONJ iajs-1988 12 14 modified modify VERB iajs-1988 12 15 tupled tuple VERB iajs-1988 12 16 coincidence coincidence NOUN iajs-1988 12 17 point point NOUN iajs-1988 12 18 with with ADP iajs-1988 12 19 study study NOUN iajs-1988 12 20 the the DET iajs-1988 12 21 existence existence NOUN iajs-1988 12 22 of of ADP iajs-1988 12 23 modified modify VERB iajs-1988 12 24 tupled tuple VERB iajs-1988 12 25 coincidence coincidence NOUN iajs-1988 12 26 point point NOUN iajs-1988 12 27 in in ADP iajs-1988 12 28 partially partially ADV iajs-1988 12 29 ordered order VERB iajs-1988 12 30 generalized generalized ADJ iajs-1988 12 31 metric metric ADJ iajs-1988 12 32 space space NOUN iajs-1988 12 33 . . PUNCT iajs-1988 13 1 2.background 2.background NUM iajs-1988 13 2 in in ADP iajs-1988 13 3 this this DET iajs-1988 13 4 section section NOUN iajs-1988 13 5 , , PUNCT iajs-1988 13 6 we we PRON iajs-1988 13 7 recall recall VERB iajs-1988 13 8 some some DET iajs-1988 13 9 definitions definition NOUN iajs-1988 13 10 and and CCONJ iajs-1988 13 11 properties property NOUN iajs-1988 13 12 introduced introduce VERB iajs-1988 13 13 by by ADP iajs-1988 13 14 mustafa mustafa PROPN iajs-1988 13 15 and and CCONJ iajs-1988 13 16 simis simis ADJ iajs-1988 13 17 [ [ X iajs-1988 13 18 2 2 NUM iajs-1988 13 19 ] ] PUNCT iajs-1988 13 20 definition definition NOUN iajs-1988 13 21 1 1 NUM iajs-1988 13 22 let let VERB iajs-1988 13 23 𝑋 𝑋 NOUN iajs-1988 13 24 beia beia NOUN iajs-1988 13 25 nonemptyiset nonemptyiset NOUN iajs-1988 13 26 , , PUNCT iajs-1988 13 27 𝒢 𝒢 PROPN iajs-1988 13 28 : : PUNCT iajs-1988 13 29 𝑋 𝑋 PROPN iajs-1988 13 30 𝑋 𝑋 PROPN iajs-1988 13 31 𝑋 𝑋 PROPN iajs-1988 13 32 → → SYM iajs-1988 13 33 𝑅 𝑅 PROPN iajs-1988 13 34 be be AUX iajs-1988 13 35 a a DET iajs-1988 13 36 function function NOUN iajs-1988 13 37 satisfying satisfy VERB iajs-1988 13 38 : : PUNCT iajs-1988 14 1 1 1 X iajs-1988 14 2 . . X iajs-1988 15 1 𝒢 𝒢 NOUN iajs-1988 15 2 𝑥 𝑥 PROPN iajs-1988 15 3 , , PUNCT iajs-1988 15 4 𝑦 𝑦 NOUN iajs-1988 15 5 , , PUNCT iajs-1988 15 6 𝑧 𝑧 PROPN iajs-1988 15 7 0 0 NUM iajs-1988 15 8 𝑖𝑓 𝑖𝑓 ADP iajs-1988 15 9 𝑥 𝑥 PROPN iajs-1988 15 10 𝑦 𝑦 NOUN iajs-1988 15 11 𝑧. 𝑧. NOUN iajs-1988 15 12 2.0 2.0 NUM iajs-1988 15 13 𝒢 𝒢 PROPN iajs-1988 15 14 𝑥 𝑥 PROPN iajs-1988 15 15 , , PUNCT iajs-1988 15 16 𝑥 𝑥 PROPN iajs-1988 15 17 , , PUNCT iajs-1988 15 18 𝑦 𝑦 NOUN iajs-1988 15 19 for for ADP iajs-1988 15 20 all all PRON iajs-1988 15 21 𝑥 𝑥 PROPN iajs-1988 15 22 , , PUNCT iajs-1988 15 23 𝑦 𝑦 NOUN iajs-1988 15 24 ∈ ∈ NOUN iajs-1988 15 25 𝑋 𝑋 NOUN iajs-1988 15 26 𝑤𝑖𝑡ℎ 𝑤𝑖𝑡ℎ NOUN iajs-1988 15 27 𝑥 𝑥 PROPN iajs-1988 15 28 𝑦. 𝑦. PROPN iajs-1988 15 29             SPACE iajs-1988 15 30 158 158 NUM iajs-1988 15 31     SPACE iajs-1988 15 32 ibn ibn PROPN iajs-1988 15 33 al al PROPN iajs-1988 15 34 - - PUNCT iajs-1988 15 35 haitham haitham PROPN iajs-1988 15 36 jour jour X iajs-1988 15 37 . . PROPN iajs-1988 15 38 for for ADP iajs-1988 15 39 pure pure ADJ iajs-1988 15 40 & & CCONJ iajs-1988 15 41 appl.sci appl.sci PROPN iajs-1988 15 42 . . PUNCT iajs-1988 15 43 ihjpas ihjpas PROPN iajs-1988 15 44 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 15 45 vol vol NOUN iajs-1988 15 46 . . PUNCT iajs-1988 16 1 32 32 NUM iajs-1988 16 2 ( ( PUNCT iajs-1988 16 3 1 1 NUM iajs-1988 16 4 ) ) PUNCT iajs-1988 16 5 2019 2019 NUM iajs-1988 16 6 3 3 NUM iajs-1988 16 7 . . PUNCT iajs-1988 17 1 𝒢 𝒢 PROPN iajs-1988 17 2 𝑥 𝑥 PROPN iajs-1988 17 3 , , PUNCT iajs-1988 17 4 𝑥 𝑥 PROPN iajs-1988 17 5 , , PUNCT iajs-1988 17 6 𝑦 𝑦 NOUN iajs-1988 17 7 𝒢 𝒢 NOUN iajs-1988 17 8 𝑥 𝑥 PROPN iajs-1988 17 9 , , PUNCT iajs-1988 17 10 𝑦 𝑦 NOUN iajs-1988 17 11 , , PUNCT iajs-1988 17 12 𝑧 𝑧 X iajs-1988 17 13 for for ADP iajs-1988 17 14 all all DET iajs-1988 17 15 𝑥 𝑥 PROPN iajs-1988 17 16 , , PUNCT iajs-1988 17 17 𝑦 𝑦 NOUN iajs-1988 17 18 , , PUNCT iajs-1988 17 19 𝑧 𝑧 DET iajs-1988 17 20 ∈ ∈ NOUN iajs-1988 17 21 𝑋 𝑋 NOUN iajs-1988 17 22 𝑤𝑖𝑡ℎ 𝑤𝑖𝑡ℎ VERB iajs-1988 17 23 𝑦 𝑦 PRON iajs-1988 17 24 𝑧 𝑧 NOUN iajs-1988 17 25 4 4 NUM iajs-1988 17 26 . . PUNCT iajs-1988 18 1 𝒢 𝒢 PROPN iajs-1988 18 2 𝑥 𝑥 PROPN iajs-1988 18 3 , , PUNCT iajs-1988 18 4 𝑦 𝑦 NOUN iajs-1988 18 5 , , PUNCT iajs-1988 18 6 𝑧 𝑧 PROPN iajs-1988 18 7 𝒢 𝒢 PROPN iajs-1988 18 8 𝑥 𝑥 PROPN iajs-1988 18 9 , , PUNCT iajs-1988 18 10 𝑧 𝑧 PROPN iajs-1988 18 11 , , PUNCT iajs-1988 18 12 𝑦 𝑦 PROPN iajs-1988 18 13 𝐺 𝐺 PROPN iajs-1988 18 14 𝑦 𝑦 PROPN iajs-1988 18 15 , , PUNCT iajs-1988 18 16 𝑧 𝑧 PROPN iajs-1988 18 17 , , PUNCT iajs-1988 18 18 𝑥 𝑥 X iajs-1988 18 19 … … PUNCT iajs-1988 18 20 . . PUNCT iajs-1988 19 1 𝑠ymmetry 𝑠ymmetry NOUN iajs-1988 19 2 in in ADP iajs-1988 19 3 all all DET iajs-1988 19 4 hree hree ADJ iajs-1988 19 5 variable variable NOUN iajs-1988 19 6 5 5 NUM iajs-1988 19 7 . . PUNCT iajs-1988 20 1 𝒢 𝒢 PRON iajs-1988 20 2 𝑥 𝑥 PROPN iajs-1988 20 3 , , PUNCT iajs-1988 20 4 𝑦 𝑦 NOUN iajs-1988 20 5 , , PUNCT iajs-1988 20 6 𝑧 𝑧 PROPN iajs-1988 20 7 𝒢 𝒢 PROPN iajs-1988 20 8 𝑥 𝑥 PROPN iajs-1988 20 9 , , PUNCT iajs-1988 20 10 𝑎 𝑎 NOUN iajs-1988 20 11 , , PUNCT iajs-1988 20 12 𝑎 𝑎 PROPN iajs-1988 20 13 𝒢 𝒢 PROPN iajs-1988 20 14 𝑎 𝑎 PROPN iajs-1988 20 15 , , PUNCT iajs-1988 20 16 𝑦 𝑦 NOUN iajs-1988 20 17 , , PUNCT iajs-1988 20 18 𝑥 𝑥 X iajs-1988 20 19 , , PUNCT iajs-1988 20 20 𝑧 𝑧 PRON iajs-1988 20 21 𝑓𝑜𝑟 𝑓𝑜𝑟 NOUN iajs-1988 20 22 𝑎𝑙𝑙 𝑎𝑙𝑙 X iajs-1988 20 23 𝑥 𝑥 PROPN iajs-1988 20 24 , , PUNCT iajs-1988 20 25 𝑦 𝑦 PROPN iajs-1988 20 26 , , PUNCT iajs-1988 20 27 𝑧 𝑧 PRON iajs-1988 20 28 , , PUNCT iajs-1988 20 29 𝑎 𝑎 PROPN iajs-1988 20 30 ∈ ∈ NOUN iajs-1988 20 31 𝑋 𝑋 NOUN iajs-1988 20 32 . . PUNCT iajs-1988 21 1 then then ADV iajs-1988 21 2 the the DET iajs-1988 21 3 function function NOUN iajs-1988 21 4 𝒢 𝒢 PROPN iajs-1988 21 5 is be AUX iajs-1988 21 6 called call VERB iajs-1988 21 7 generalized generalized ADJ iajs-1988 21 8 metric metric ADJ iajs-1988 21 9 and and CCONJ iajs-1988 21 10 the the DET iajs-1988 21 11 pair pair NOUN iajs-1988 21 12 ( ( PUNCT iajs-1988 21 13 x x NOUN iajs-1988 21 14 , , PUNCT iajs-1988 21 15 𝒢 𝒢 NOUN iajs-1988 21 16 ) ) PUNCT iajs-1988 21 17 is be AUX iajs-1988 21 18 called call VERB iajs-1988 21 19 a a DET iajs-1988 21 20 generalized generalize VERB iajs-1988 21 21 metric metric ADJ iajs-1988 21 22 space space NOUN iajs-1988 21 23 or or CCONJ iajs-1988 21 24 more more ADJ iajs-1988 21 25 specially specially ADV iajs-1988 21 26 𝒢 𝒢 ADJ iajs-1988 21 27 _ _ NOUN iajs-1988 21 28 metric metric ADJ iajs-1988 21 29 space space NOUN iajs-1988 21 30 . . PUNCT iajs-1988 22 1 definition definition NOUN iajs-1988 22 2 2 2 NUM iajs-1988 22 3 let let VERB iajs-1988 22 4 ( ( PUNCT iajs-1988 22 5 x x NOUN iajs-1988 22 6 , , PUNCT iajs-1988 22 7 𝒢 𝒢 NOUN iajs-1988 22 8 ) ) PUNCT iajs-1988 22 9 be be AUX iajs-1988 22 10 ai𝒢 ai𝒢 PROPN iajs-1988 22 11 _ _ NOUN iajs-1988 22 12 metricispace metricispace NOUN iajs-1988 22 13 , , PUNCT iajs-1988 22 14 and and CCONJ iajs-1988 22 15 let let VERB iajs-1988 22 16 𝑥 𝑥 PRON iajs-1988 22 17 be be AUX iajs-1988 22 18 a a DET iajs-1988 22 19 sequence sequence NOUN iajs-1988 22 20 of of ADP iajs-1988 22 21 points point NOUN iajs-1988 22 22 of of ADP iajs-1988 22 23 𝑋.we 𝑋.we NOUN iajs-1988 22 24 say say VERB iajs-1988 22 25 that that SCONJ iajs-1988 22 26 𝑥 𝑥 PROPN iajs-1988 22 27 is be AUX iajs-1988 22 28 𝒢_convergentito 𝒢_convergentito X iajs-1988 22 29 𝑥 𝑥 X iajs-1988 22 30 if if SCONJ iajs-1988 22 31 lim lim PROPN iajs-1988 22 32 , , PUNCT iajs-1988 22 33 → → PUNCT iajs-1988 22 34 𝒢 𝒢 PROPN iajs-1988 22 35 𝑥 𝑥 PROPN iajs-1988 22 36 , , PUNCT iajs-1988 22 37 𝑥 𝑥 X iajs-1988 22 38 , , PUNCT iajs-1988 22 39 𝑥 𝑥 PROPN iajs-1988 22 40 0 0 NUM iajs-1988 22 41 , , PUNCT iajs-1988 22 42 thatiis thatiis NOUN iajs-1988 22 43 , , PUNCT iajs-1988 22 44 for for ADP iajs-1988 22 45 any any DET iajs-1988 22 46 𝜀 𝜀 NOUN iajs-1988 22 47 0 0 NUM iajs-1988 22 48 there there PRON iajs-1988 22 49 exist exist VERB iajs-1988 22 50 𝑁 𝑁 PROPN iajs-1988 22 51 ∈ ∈ PROPN iajs-1988 22 52 ℕ ℕ NOUN iajs-1988 22 53 such such ADJ iajs-1988 22 54 that that SCONJ iajs-1988 22 55 𝒢 𝒢 PROPN iajs-1988 22 56 𝑥 𝑥 PROPN iajs-1988 22 57 , , PUNCT iajs-1988 22 58 𝑥 𝑥 PROPN iajs-1988 22 59 , , PUNCT iajs-1988 22 60 𝑥 𝑥 DET iajs-1988 22 61 𝜀 𝜀 NOUN iajs-1988 22 62 , , PUNCT iajs-1988 22 63 for for ADP iajs-1988 22 64 all all DET iajs-1988 22 65 𝑛 𝑛 PROPN iajs-1988 22 66 , , PUNCT iajs-1988 22 67 𝑚 𝑚 X iajs-1988 22 68 𝑁.we 𝑁.we NOUN iajs-1988 22 69 call call VERB iajs-1988 22 70 𝑥 𝑥 ADP iajs-1988 22 71 the the DET iajs-1988 22 72 limit limit NOUN iajs-1988 22 73 of of ADP iajs-1988 22 74 sequence sequence NOUN iajs-1988 22 75 and and CCONJ iajs-1988 22 76 write write VERB iajs-1988 22 77 𝑥 𝑥 PROPN iajs-1988 22 78 → → SYM iajs-1988 22 79 𝑥 𝑥 PROPN iajs-1988 22 80 or or CCONJ iajs-1988 22 81 lim lim PROPN iajs-1988 22 82 , , PUNCT iajs-1988 22 83 → → SYM iajs-1988 22 84 𝑥 𝑥 X iajs-1988 22 85 𝑥. 𝑥. ADJ iajs-1988 22 86 definition definition NOUN iajs-1988 22 87 3 3 NUM iajs-1988 22 88 let let VERB iajs-1988 22 89 ( ( PUNCT iajs-1988 22 90 x x NOUN iajs-1988 22 91 , , PUNCT iajs-1988 22 92 𝒢 𝒢 NOUN iajs-1988 22 93 ) ) PUNCT iajs-1988 22 94 be be AUX iajs-1988 22 95 a a DET iajs-1988 22 96 𝒢 𝒢 PROPN iajs-1988 22 97 _ _ NOUN iajs-1988 22 98 metric metric ADJ iajs-1988 22 99 space space NOUN iajs-1988 22 100 , , PUNCT iajs-1988 22 101 a a DET iajs-1988 22 102 sequence sequence NOUN iajs-1988 22 103 𝑥 𝑥 NOUN iajs-1988 22 104 is be AUX iajs-1988 22 105 called call VERB iajs-1988 22 106 𝒢_cauchy 𝒢_cauchy NOUN iajs-1988 22 107 sequence sequence NOUN iajs-1988 22 108 if if SCONJ iajs-1988 22 109 for for ADP iajs-1988 22 110 any any DET iajs-1988 22 111 𝜀 𝜀 NOUN iajs-1988 22 112 0 0 NUM iajs-1988 22 113 there there PRON iajs-1988 22 114 exist exist VERB iajs-1988 22 115 𝑁 𝑁 PROPN iajs-1988 22 116 ∈ ∈ PROPN iajs-1988 22 117 ℕ ℕ NOUN iajs-1988 22 118 such such ADJ iajs-1988 22 119 that that SCONJ iajs-1988 22 120 𝒢 𝒢 PROPN iajs-1988 22 121 𝑥 𝑥 PROPN iajs-1988 22 122 , , PUNCT iajs-1988 22 123 𝑥 𝑥 X iajs-1988 22 124 , , PUNCT iajs-1988 22 125 𝑥 𝑥 DET iajs-1988 22 126 𝜀 𝜀 NOUN iajs-1988 22 127 for for ADP iajs-1988 22 128 all all DET iajs-1988 22 129 𝑛 𝑛 PROPN iajs-1988 22 130 , , PUNCT iajs-1988 22 131 𝑚 𝑚 PROPN iajs-1988 22 132 , , PUNCT iajs-1988 22 133 𝑙 𝑙 PROPN iajs-1988 22 134 𝑁 𝑁 PROPN iajs-1988 22 135 , , PUNCT iajs-1988 22 136 that that ADV iajs-1988 22 137 is is ADV iajs-1988 22 138 , , PUNCT iajs-1988 22 139 𝒢 𝒢 PROPN iajs-1988 22 140 𝑥 𝑥 X iajs-1988 22 141 , , PUNCT iajs-1988 22 142 𝑥 𝑥 X iajs-1988 22 143 , , PUNCT iajs-1988 22 144 𝑥 𝑥 X iajs-1988 22 145 → → SYM iajs-1988 22 146 0 0 NUM iajs-1988 22 147 𝑎𝑠 𝑎𝑠 PROPN iajs-1988 22 148 𝑛 𝑛 PROPN iajs-1988 22 149 , , PUNCT iajs-1988 22 150 𝑚 𝑚 PROPN iajs-1988 22 151 , , PUNCT iajs-1988 22 152 𝑙 𝑙 X iajs-1988 22 153 → → SYM iajs-1988 22 154 ∞ ∞ NUM iajs-1988 22 155 . . PUNCT iajs-1988 23 1 proposition proposition NOUN iajs-1988 23 2 4 4 NUM iajs-1988 23 3 let let VERB iajs-1988 23 4 ( ( PUNCT iajs-1988 23 5 x x NOUN iajs-1988 23 6 , , PUNCT iajs-1988 23 7 𝒢 𝒢 NOUN iajs-1988 23 8 ) ) PUNCT iajs-1988 23 9 be be AUX iajs-1988 23 10 a a DET iajs-1988 23 11 𝐺 𝐺 NOUN iajs-1988 23 12 _ _ NOUN iajs-1988 23 13 metricispace metricispace NOUN iajs-1988 23 14 . . PUNCT iajs-1988 24 1 a a DET iajs-1988 24 2 mapping mapping NOUN iajs-1988 24 3 is be AUX iajs-1988 24 4 called call VERB iajs-1988 24 5 𝒢_continuousiat 𝒢_continuousiat PUNCT iajs-1988 24 6 𝑥 𝑥 PRON iajs-1988 24 7 ∈ ∈ NOUN iajs-1988 24 8 𝑋 𝑋 NOUN iajs-1988 24 9 if if SCONJ iajs-1988 24 10 and and CCONJ iajs-1988 24 11 if if SCONJ iajs-1988 24 12 it it PRON iajs-1988 24 13 is be AUX iajs-1988 24 14 𝒢_sequentiallycontinuous 𝒢_sequentiallycontinuous ADJ iajs-1988 24 15 at at ADP iajs-1988 24 16 𝑥 𝑥 NOUN iajs-1988 24 17 , , PUNCT iajs-1988 24 18 that that ADV iajs-1988 24 19 is is ADV iajs-1988 24 20 , , PUNCT iajs-1988 24 21 wheneveri wheneveri PROPN iajs-1988 24 22 𝑥 𝑥 PROPN iajs-1988 24 23 is be AUX iajs-1988 24 24 𝒢_convergentito 𝒢_convergentito PROPN iajs-1988 24 25 𝑥 𝑥 PROPN iajs-1988 24 26 , , PUNCT iajs-1988 24 27 𝑓 𝑓 PRON iajs-1988 25 1 𝑥 𝑥 X iajs-1988 25 2 𝑖𝑠 𝑖𝑠 ADJ iajs-1988 25 3 𝒢_convergentito 𝒢_convergentito PROPN iajs-1988 25 4 𝑓 𝑓 PROPN iajs-1988 25 5 𝑥 𝑥 PROPN iajs-1988 25 6 . . PUNCT iajs-1988 26 1 proposition proposition NOUN iajs-1988 26 2 5 5 NUM iajs-1988 26 3 a a DET iajs-1988 26 4 𝒢 𝒢 PROPN iajs-1988 26 5 _ _ NOUN iajs-1988 26 6 metric metric ADJ iajs-1988 26 7 space space NOUN iajs-1988 26 8 ( ( PUNCT iajs-1988 26 9 x x NOUN iajs-1988 26 10 , , PUNCT iajs-1988 26 11 𝒢 𝒢 NOUN iajs-1988 26 12 ) ) PUNCT iajs-1988 26 13 is be AUX iajs-1988 26 14 called call VERB iajs-1988 26 15 𝐺_completeiif 𝐺_completeiif PROPN iajs-1988 26 16 every every DET iajs-1988 26 17 𝒢_cauchyisequence 𝒢_cauchyisequence NOUN iajs-1988 26 18 is be AUX iajs-1988 26 19 𝒢_convergentiin 𝒢_convergentiin NOUN iajs-1988 26 20 ( ( PUNCT iajs-1988 26 21 x x NOUN iajs-1988 26 22 , , PUNCT iajs-1988 26 23 𝒢 𝒢 PROPN iajs-1988 26 24 ) ) PUNCT iajs-1988 26 25 . . PUNCT iajs-1988 27 1 3 3 X iajs-1988 27 2 . . X iajs-1988 27 3 main main ADJ iajs-1988 27 4 results result NOUN iajs-1988 27 5 in in ADP iajs-1988 27 6 this this DET iajs-1988 27 7 section section NOUN iajs-1988 27 8 , , PUNCT iajs-1988 27 9 the the DET iajs-1988 27 10 modification modification NOUN iajs-1988 27 11 of of ADP iajs-1988 27 12 tupled tuple VERB iajs-1988 27 13 coincidence coincidence NOUN iajs-1988 27 14 point point NOUN iajs-1988 27 15 is be AUX iajs-1988 27 16 proposed propose VERB iajs-1988 27 17 as as ADP iajs-1988 27 18 the the DET iajs-1988 27 19 follows follow NOUN iajs-1988 27 20 : : PUNCT iajs-1988 27 21 definition definition NOUN iajs-1988 27 22 6 6 NUM iajs-1988 27 23 let let VERB iajs-1988 27 24 𝑋 𝑋 PROPN iajs-1988 27 25 , , PUNCT iajs-1988 27 26 be be AUX iajs-1988 27 27 a a DET iajs-1988 27 28 partiallyiordered partiallyiordere VERB iajs-1988 27 29 set set NOUN iajs-1988 27 30 . . PUNCT iajs-1988 28 1 if if SCONJ iajs-1988 28 2 𝒯 𝒯 PROPN iajs-1988 28 3 : : PUNCT iajs-1988 28 4 𝑋 𝑋 PROPN iajs-1988 28 5 → → SYM iajs-1988 28 6 𝑋 𝑋 PROPN iajs-1988 28 7 , , PUNCT iajs-1988 28 8 𝒯 𝒯 PROPN iajs-1988 28 9 , , PUNCT iajs-1988 28 10 𝒯 𝒯 PROPN iajs-1988 28 11 , , PUNCT iajs-1988 28 12 … … PUNCT iajs-1988 28 13 , , PUNCT iajs-1988 28 14 𝒯 𝒯 PROPN iajs-1988 28 15 , , PUNCT iajs-1988 28 16 𝒰 𝒰 PROPN iajs-1988 28 17 , , PUNCT iajs-1988 28 18 𝒱 𝒱 PROPN iajs-1988 28 19 : : PUNCT iajs-1988 28 20 𝑋 𝑋 PROPN iajs-1988 28 21 → → SYM iajs-1988 28 22 𝑋 𝑋 PROPN iajs-1988 28 23 are be AUX iajs-1988 28 24 there there PRON iajs-1988 28 25 mappings mapping NOUN iajs-1988 28 26 . . PUNCT iajs-1988 29 1 an an DET iajs-1988 29 2 element element NOUN iajs-1988 29 3 𝑥 𝑥 NOUN iajs-1988 29 4 , , PUNCT iajs-1988 29 5 𝑥 𝑥 X iajs-1988 29 6 , , PUNCT iajs-1988 29 7 … … PUNCT iajs-1988 29 8 … … PUNCT iajs-1988 29 9 , , PUNCT iajs-1988 29 10 𝑥 𝑥 PRON iajs-1988 29 11 ∈ ∈ PROPN iajs-1988 29 12 𝑋 𝑋 NOUN iajs-1988 29 13 is be AUX iajs-1988 29 14 called call VERB iajs-1988 29 15 modified modified ADJ iajs-1988 29 16 tupled tuple VERB iajs-1988 29 17 coincidence coincidence NOUN iajs-1988 29 18 point point NOUN iajs-1988 29 19 of of ADP iajs-1988 29 20 𝒯 𝒯 PROPN iajs-1988 29 21 , , PUNCT iajs-1988 29 22 𝒯 𝒯 PROPN iajs-1988 29 23 , , PUNCT iajs-1988 29 24 … … PUNCT iajs-1988 29 25 𝒯 𝒯 PROPN iajs-1988 29 26 , , PUNCT iajs-1988 29 27 𝒰 𝒰 PROPN iajs-1988 29 28 and and CCONJ iajs-1988 29 29 𝒱 𝒱 PROPN iajs-1988 30 1 if if SCONJ iajs-1988 30 2 : : PUNCT iajs-1988 30 3 𝒯 𝒯 PROPN iajs-1988 30 4 𝒯 𝒯 PROPN iajs-1988 30 5 … … PUNCT iajs-1988 30 6 𝒯 𝒯 PROPN iajs-1988 30 7 𝑥 𝑥 PROPN iajs-1988 30 8 , , PUNCT iajs-1988 30 9 𝑥 𝑥 X iajs-1988 30 10 , , PUNCT iajs-1988 30 11 … … PUNCT iajs-1988 30 12 … … PUNCT iajs-1988 30 13 , , PUNCT iajs-1988 30 14 𝑥 𝑥 DET iajs-1988 30 15 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 30 16 𝑥 𝑥 PROPN iajs-1988 30 17 𝒯 𝒯 PROPN iajs-1988 30 18 𝒯 𝒯 PROPN iajs-1988 30 19 … … PUNCT iajs-1988 30 20 𝒯 𝒯 PROPN iajs-1988 30 21 𝑥 𝑥 PROPN iajs-1988 30 22 , , PUNCT iajs-1988 30 23 𝑥 𝑥 X iajs-1988 30 24 , , PUNCT iajs-1988 30 25 … … PUNCT iajs-1988 30 26 … … PUNCT iajs-1988 30 27 , , PUNCT iajs-1988 30 28 𝑥 𝑥 X iajs-1988 30 29 , , PUNCT iajs-1988 30 30 𝑥 𝑥 PRON iajs-1988 30 31 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 30 32 𝑥 𝑥 NOUN iajs-1988 30 33 ⋮ ⋮ NOUN iajs-1988 30 34 𝒯 𝒯 PROPN iajs-1988 30 35 𝒯 𝒯 PROPN iajs-1988 30 36 … … PUNCT iajs-1988 30 37 𝒯 𝒯 PROPN iajs-1988 30 38 𝑥 𝑥 PROPN iajs-1988 30 39 , , PUNCT iajs-1988 30 40 𝑥 𝑥 X iajs-1988 30 41 , , PUNCT iajs-1988 30 42 … … PUNCT iajs-1988 30 43 … … PUNCT iajs-1988 30 44 , , PUNCT iajs-1988 30 45 𝑥 𝑥 DET iajs-1988 30 46 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 30 47 𝑥 𝑥 PROPN iajs-1988 30 48             SPACE iajs-1988 30 49 159 159 NUM iajs-1988 30 50     SPACE iajs-1988 30 51 ibn ibn PROPN iajs-1988 30 52 al al PROPN iajs-1988 30 53 - - PUNCT iajs-1988 30 54 haitham haitham PROPN iajs-1988 30 55 jour jour X iajs-1988 30 56 . . PROPN iajs-1988 31 1 for for ADP iajs-1988 31 2 pure pure ADJ iajs-1988 31 3 & & CCONJ iajs-1988 31 4 appl.sci appl.sci PROPN iajs-1988 31 5 . . PUNCT iajs-1988 32 1 ihjpas ihjpas PROPN iajs-1988 32 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 32 3 vol vol NOUN iajs-1988 32 4 . . PUNCT iajs-1988 33 1 32 32 NUM iajs-1988 33 2 ( ( PUNCT iajs-1988 33 3 1 1 NUM iajs-1988 33 4 ) ) SYM iajs-1988 33 5 2019 2019 NUM iajs-1988 33 6 definition definition NOUN iajs-1988 33 7 7 7 NUM iajs-1988 33 8 let let VERB iajs-1988 33 9 𝑋 𝑋 PROPN iajs-1988 33 10 , , PUNCT iajs-1988 33 11 be be AUX iajs-1988 33 12 a a DET iajs-1988 33 13 partiallyiordered partiallyiordere VERB iajs-1988 33 14 set set NOUN iajs-1988 33 15 . . PUNCT iajs-1988 34 1 if if SCONJ iajs-1988 34 2 𝒯 𝒯 PROPN iajs-1988 34 3 : : PUNCT iajs-1988 34 4 𝑋 𝑋 PROPN iajs-1988 34 5 → → SYM iajs-1988 34 6 𝑋 𝑋 PROPN iajs-1988 34 7 , , PUNCT iajs-1988 34 8 𝒯 𝒯 PROPN iajs-1988 34 9 , , PUNCT iajs-1988 34 10 𝒯 𝒯 PROPN iajs-1988 34 11 , , PUNCT iajs-1988 34 12 … … PUNCT iajs-1988 34 13 , , PUNCT iajs-1988 34 14 𝒯 𝒯 PROPN iajs-1988 34 15 , , PUNCT iajs-1988 34 16 𝒰 𝒰 PROPN iajs-1988 34 17 , , PUNCT iajs-1988 34 18 𝒱 𝒱 PROPN iajs-1988 34 19 : : PUNCT iajs-1988 34 20 𝑋 𝑋 PROPN iajs-1988 34 21 → → SYM iajs-1988 34 22 𝑋 𝑋 PROPN iajs-1988 34 23 are be AUX iajs-1988 34 24 there there ADV iajs-1988 34 25 mappingsiwe mappingsiwe ADJ iajs-1988 34 26 say say VERB iajs-1988 34 27 that that SCONJ iajs-1988 34 28 𝑓 𝑓 PROPN iajs-1988 34 29 have have VERB iajs-1988 34 30 mixedifinite mixedifinite NOUN iajs-1988 34 31 monotone monotone ADJ iajs-1988 34 32 property property NOUN iajs-1988 34 33 if if SCONJ iajs-1988 34 34 𝒯 𝒯 PROPN iajs-1988 34 35 𝒯 𝒯 PROPN iajs-1988 34 36 … … PUNCT iajs-1988 34 37 𝒯 𝒯 PROPN iajs-1988 34 38 𝑥 𝑥 PROPN iajs-1988 34 39 , , PUNCT iajs-1988 34 40 𝑥 𝑥 X iajs-1988 34 41 , , PUNCT iajs-1988 34 42 … … PUNCT iajs-1988 34 43 … … PUNCT iajs-1988 34 44 , , PUNCT iajs-1988 34 45 𝑥 𝑥 PROPN iajs-1988 34 46 is be AUX iajs-1988 34 47 monotoneifinite monotoneifinite NOUN iajs-1988 34 48 increasing increase VERB iajs-1988 34 49 if if SCONJ iajs-1988 34 50 𝑛 𝑛 PRON iajs-1988 34 51 is be AUX iajs-1988 34 52 odd odd ADJ iajs-1988 34 53 , , PUNCT iajs-1988 34 54 and and CCONJ iajs-1988 34 55 𝒯 𝒯 PROPN iajs-1988 34 56 𝒯 𝒯 PROPN iajs-1988 34 57 … … PUNCT iajs-1988 34 58 𝒯 𝒯 PROPN iajs-1988 34 59 𝑥 𝑥 PROPN iajs-1988 34 60 , , PUNCT iajs-1988 34 61 𝑥 𝑥 X iajs-1988 34 62 , , PUNCT iajs-1988 34 63 … … PUNCT iajs-1988 34 64 … … PUNCT iajs-1988 34 65 , , PUNCT iajs-1988 34 66 𝑥 𝑥 PROPN iajs-1988 34 67 is be AUX iajs-1988 34 68 monotone monotone ADJ iajs-1988 34 69 finite finite NOUN iajs-1988 34 70 decreasingiif decreasingiif X iajs-1988 34 71 𝑛 𝑛 PRON iajs-1988 34 72 is be AUX iajs-1988 34 73 even even ADV iajs-1988 34 74 that that ADV iajs-1988 34 75 is is ADV iajs-1988 34 76 , , PUNCT iajs-1988 34 77 forieach forieach VERB iajs-1988 34 78 𝑥 𝑥 PRON iajs-1988 34 79 , , PUNCT iajs-1988 34 80 𝑥 𝑥 X iajs-1988 34 81 , , PUNCT iajs-1988 34 82 … … PUNCT iajs-1988 34 83 … … PUNCT iajs-1988 34 84 , , PUNCT iajs-1988 34 85 𝑥 𝑥 PRON iajs-1988 34 86 ∈ ∈ PROPN iajs-1988 34 87 𝑋 𝑋 PROPN iajs-1988 34 88 𝑦 𝑦 NOUN iajs-1988 34 89 , , PUNCT iajs-1988 34 90 𝑧 𝑧 DET iajs-1988 34 91 ∈ ∈ PROPN iajs-1988 34 92 𝑋 𝑋 PROPN iajs-1988 34 93 , , PUNCT iajs-1988 34 94 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 95 𝑦 𝑦 PROPN iajs-1988 34 96 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 97 𝑧 𝑧 VERB iajs-1988 34 98 ⟹ ⟹ NUM iajs-1988 34 99 𝒯 𝒯 PROPN iajs-1988 34 100 𝒯 𝒯 PROPN iajs-1988 34 101 … … PUNCT iajs-1988 34 102 𝒯 𝒯 PROPN iajs-1988 34 103 𝑦 𝑦 PROPN iajs-1988 34 104 , , PUNCT iajs-1988 34 105 𝑥 𝑥 X iajs-1988 34 106 , , PUNCT iajs-1988 34 107 𝑥 𝑥 X iajs-1988 34 108 , , PUNCT iajs-1988 34 109 … … PUNCT iajs-1988 34 110 , , PUNCT iajs-1988 34 111 𝑥 𝑥 PROPN iajs-1988 34 112 𝒯 𝒯 PROPN iajs-1988 34 113 𝒯 𝒯 PROPN iajs-1988 34 114 … … PUNCT iajs-1988 34 115 𝒯 𝒯 PROPN iajs-1988 34 116 𝑧 𝑧 PROPN iajs-1988 34 117 , , PUNCT iajs-1988 34 118 𝑥 𝑥 X iajs-1988 34 119 , , PUNCT iajs-1988 34 120 𝑥 𝑥 X iajs-1988 34 121 , , PUNCT iajs-1988 34 122 … … PUNCT iajs-1988 34 123 , , PUNCT iajs-1988 34 124 𝑥 𝑥 PRON iajs-1988 34 125 𝑦 𝑦 NOUN iajs-1988 34 126 , , PUNCT iajs-1988 34 127 𝑧 𝑧 DET iajs-1988 34 128 ∈ ∈ PROPN iajs-1988 34 129 𝑋 𝑋 PROPN iajs-1988 34 130 , , PUNCT iajs-1988 34 131 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 132 𝑦 𝑦 PROPN iajs-1988 34 133 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 134 𝑧 𝑧 VERB iajs-1988 34 135 ⟹ ⟹ NUM iajs-1988 34 136 𝒯 𝒯 PROPN iajs-1988 34 137 𝒯 𝒯 PROPN iajs-1988 34 138 … … PUNCT iajs-1988 34 139 𝒯 𝒯 PROPN iajs-1988 34 140 𝑥 𝑥 PROPN iajs-1988 34 141 , , PUNCT iajs-1988 34 142 𝑦 𝑦 NOUN iajs-1988 34 143 , , PUNCT iajs-1988 34 144 𝑥 𝑥 X iajs-1988 34 145 , , PUNCT iajs-1988 34 146 … … PUNCT iajs-1988 34 147 , , PUNCT iajs-1988 34 148 𝑥 𝑥 PROPN iajs-1988 34 149 𝒯 𝒯 PROPN iajs-1988 34 150 𝒯 𝒯 PROPN iajs-1988 34 151 … … PUNCT iajs-1988 34 152 𝒯 𝒯 PROPN iajs-1988 34 153 𝑥 𝑥 PROPN iajs-1988 34 154 , , PUNCT iajs-1988 34 155 𝑧 𝑧 PROPN iajs-1988 34 156 , , PUNCT iajs-1988 34 157 𝑥 𝑥 X iajs-1988 34 158 , , PUNCT iajs-1988 34 159 … … PUNCT iajs-1988 34 160 , , PUNCT iajs-1988 34 161 𝑥 𝑥 PRON iajs-1988 34 162 ⋮ ⋮ NOUN iajs-1988 34 163 𝑦 𝑦 NOUN iajs-1988 34 164 , , PUNCT iajs-1988 34 165 𝑧 𝑧 DET iajs-1988 34 166 ∈ ∈ PROPN iajs-1988 34 167 𝑋 𝑋 PROPN iajs-1988 34 168 , , PUNCT iajs-1988 34 169 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 170 𝑦 𝑦 PROPN iajs-1988 34 171 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 34 172 𝑧 𝑧 VERB iajs-1988 34 173 ⟹ ⟹ NUM iajs-1988 34 174 𝒯 𝒯 PROPN iajs-1988 34 175 𝒯 𝒯 PROPN iajs-1988 34 176 … … PUNCT iajs-1988 34 177 𝒯 𝒯 PROPN iajs-1988 34 178 𝑥 𝑥 PROPN iajs-1988 34 179 , , PUNCT iajs-1988 34 180 𝑥 𝑥 X iajs-1988 34 181 , , PUNCT iajs-1988 34 182 … … PUNCT iajs-1988 34 183 , , PUNCT iajs-1988 34 184 𝑦 𝑦 X iajs-1988 34 185 𝒯 𝒯 PROPN iajs-1988 34 186 𝒯 𝒯 PROPN iajs-1988 34 187 … … PUNCT iajs-1988 34 188 𝒯 𝒯 PROPN iajs-1988 34 189 𝑥 𝑥 PROPN iajs-1988 34 190 , , PUNCT iajs-1988 34 191 𝑥 𝑥 X iajs-1988 34 192 , , PUNCT iajs-1988 34 193 … … PUNCT iajs-1988 34 194 , , PUNCT iajs-1988 34 195 𝑧 𝑧 PROPN iajs-1988 34 196 𝑖𝑓 𝑖𝑓 NOUN iajs-1988 34 197 𝑛 𝑛 PRON iajs-1988 34 198 𝑖𝑠 𝑖𝑠 NOUN iajs-1988 34 199 𝑜𝑑𝑑 𝑜𝑑𝑑 NOUN iajs-1988 35 1 𝒯 𝒯 PROPN iajs-1988 35 2 𝒯 𝒯 PROPN iajs-1988 35 3 … … PUNCT iajs-1988 35 4 𝒯 𝒯 PROPN iajs-1988 35 5 𝑥 𝑥 PROPN iajs-1988 35 6 , , PUNCT iajs-1988 35 7 𝑥 𝑥 X iajs-1988 35 8 , , PUNCT iajs-1988 35 9 … … PUNCT iajs-1988 35 10 , , PUNCT iajs-1988 35 11 𝑦 𝑦 X iajs-1988 35 12 𝒯 𝒯 PROPN iajs-1988 35 13 𝒯 𝒯 PROPN iajs-1988 35 14 … … PUNCT iajs-1988 35 15 𝒯 𝒯 PROPN iajs-1988 35 16 𝑥 𝑥 PROPN iajs-1988 35 17 , , PUNCT iajs-1988 35 18 𝑥 𝑥 X iajs-1988 35 19 , , PUNCT iajs-1988 35 20 … … PUNCT iajs-1988 35 21 , , PUNCT iajs-1988 35 22 𝑧 𝑧 PROPN iajs-1988 35 23 𝑖𝑓 𝑖𝑓 NOUN iajs-1988 35 24 𝑛 𝑛 PRON iajs-1988 35 25 𝑖𝑠 𝑖𝑠 INTJ iajs-1988 35 26 𝑒𝑣𝑒𝑛 𝑒𝑣𝑒𝑛 INTJ iajs-1988 35 27 let let VERB iajs-1988 35 28 i. i. PROPN iajs-1988 35 29 𝒜 𝒜 PROPN iajs-1988 35 30 is be AUX iajs-1988 35 31 the the DET iajs-1988 35 32 setiof setiof NOUN iajs-1988 35 33 all all DET iajs-1988 35 34 mappings mapping NOUN iajs-1988 36 1 𝒯 𝒯 PROPN iajs-1988 36 2 : : PUNCT iajs-1988 36 3 𝑋 𝑋 PROPN iajs-1988 36 4 → → SYM iajs-1988 36 5 𝑋 𝑋 PROPN iajs-1988 36 6 and and CCONJ iajs-1988 36 7 𝒯 𝒯 PROPN iajs-1988 36 8 , , PUNCT iajs-1988 36 9 𝒯 𝒯 PROPN iajs-1988 36 10 , , PUNCT iajs-1988 36 11 … … PUNCT iajs-1988 36 12 , , PUNCT iajs-1988 36 13 𝒯 𝒯 PROPN iajs-1988 36 14 , , PUNCT iajs-1988 36 15 𝒰 𝒰 PROPN iajs-1988 36 16 and and CCONJ iajs-1988 36 17 𝒱 𝒱 PROPN iajs-1988 36 18 ∶ ∶ NOUN iajs-1988 36 19 𝑋 𝑋 NOUN iajs-1988 36 20 → → PUNCT iajs-1988 36 21 𝑋 𝑋 PROPN iajs-1988 36 22 such such ADJ iajs-1988 36 23 that that PRON iajs-1988 36 24 : : PUNCT iajs-1988 36 25 1 1 X iajs-1988 36 26 . . X iajs-1988 36 27 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 36 28 𝑋 𝑋 PROPN iajs-1988 36 29 is be AUX iajs-1988 36 30 completeisubspace completeisubspace NOUN iajs-1988 36 31 of of ADP iajs-1988 36 32 𝑋 𝑋 PROPN iajs-1988 36 33 , , PUNCT iajs-1988 36 34 containing contain VERB iajs-1988 36 35 𝒯 𝒯 PROPN iajs-1988 36 36 𝒯 𝒯 PROPN iajs-1988 36 37 … … PUNCT iajs-1988 36 38 𝒯 𝒯 PROPN iajs-1988 36 39 𝑋 𝑋 PROPN iajs-1988 36 40 2 2 NUM iajs-1988 36 41 . . PUNCT iajs-1988 37 1 𝒯 𝒯 PROPN iajs-1988 37 2 , , PUNCT iajs-1988 37 3 𝒯 𝒯 PROPN iajs-1988 37 4 , , PUNCT iajs-1988 37 5 … … PUNCT iajs-1988 37 6 , , PUNCT iajs-1988 37 7 𝒯 𝒯 PROPN iajs-1988 37 8 , , PUNCT iajs-1988 37 9 𝒰 𝒰 PROPN iajs-1988 37 10 and and CCONJ iajs-1988 37 11 𝒱 𝒱 PROPN iajs-1988 37 12 are be AUX iajs-1988 37 13 continuousiand continuousiand NOUN iajs-1988 37 14 commuteimappings commuteimapping NOUN iajs-1988 37 15 . . PUNCT iajs-1988 38 1 3 3 X iajs-1988 38 2 . . X iajs-1988 38 3 𝒯 𝒯 PROPN iajs-1988 38 4 , , PUNCT iajs-1988 38 5 𝒯 𝒯 PROPN iajs-1988 38 6 , , PUNCT iajs-1988 38 7 … … PUNCT iajs-1988 38 8 , , PUNCT iajs-1988 38 9 𝒯 𝒯 PROPN iajs-1988 38 10 , , PUNCT iajs-1988 38 11 have have VERB iajs-1988 38 12 mixed mix VERB iajs-1988 38 13 finite finite ADJ iajs-1988 38 14 monotone monotone ADJ iajs-1988 38 15 property property NOUN iajs-1988 38 16 . . PUNCT iajs-1988 39 1 ii ii PROPN iajs-1988 39 2 . . PUNCT iajs-1988 40 1 𝔅 𝔅 PROPN iajs-1988 40 2 is be AUX iajs-1988 40 3 the the DET iajs-1988 40 4 set set NOUN iajs-1988 40 5 of of ADP iajs-1988 40 6 all all DET iajs-1988 40 7 mappings mapping NOUN iajs-1988 40 8 𝜔 𝜔 NUM iajs-1988 40 9 : : PUNCT iajs-1988 40 10 0 0 NUM iajs-1988 40 11 , , PUNCT iajs-1988 40 12 ∞ ∞ PROPN iajs-1988 40 13 → → SYM iajs-1988 40 14 0 0 NUM iajs-1988 40 15 , , PUNCT iajs-1988 40 16 ∞ ∞ NOUN iajs-1988 40 17 increasing increase VERB iajs-1988 40 18 mapping mapping NOUN iajs-1988 40 19 such such ADJ iajs-1988 40 20 that that SCONJ iajs-1988 40 21 : : PUNCT iajs-1988 40 22 1 1 X iajs-1988 40 23 . . X iajs-1988 40 24 𝜔 𝜔 PART iajs-1988 40 25 𝑡 𝑡 PROPN iajs-1988 40 26 𝑡 𝑡 X iajs-1988 40 27 ∀ ∀ X iajs-1988 40 28 𝑡 𝑡 X iajs-1988 40 29 0 0 NUM iajs-1988 40 30 2 2 NUM iajs-1988 40 31 . . PUNCT iajs-1988 40 32 𝜔 𝜔 SYM iajs-1988 40 33 0 0 NUM iajs-1988 40 34 0 0 NUM iajs-1988 40 35 𝑎𝑛𝑑 𝑎𝑛𝑑 PROPN iajs-1988 40 36 lim lim PROPN iajs-1988 40 37 → → SYM iajs-1988 40 38 𝜔 𝜔 X iajs-1988 40 39 𝑡 𝑡 X iajs-1988 40 40 0 0 NUM iajs-1988 40 41 , , PUNCT iajs-1988 40 42 where where SCONJ iajs-1988 40 43 𝜔 𝜔 AUX iajs-1988 40 44 denotes denote NOUN iajs-1988 40 45 the the DET iajs-1988 40 46 𝑛 𝑛 PRON iajs-1988 40 47 the the DET iajs-1988 40 48 iterate iterate NOUN iajs-1988 40 49 of of ADP iajs-1988 40 50 𝜔. 𝜔. NOUN iajs-1988 40 51 from from ADP iajs-1988 40 52 the the DET iajs-1988 40 53 above above ADJ iajs-1988 40 54 definition definition NOUN iajs-1988 40 55 , , PUNCT iajs-1988 40 56 we we PRON iajs-1988 40 57 show show VERB iajs-1988 40 58 the the DET iajs-1988 40 59 following follow VERB iajs-1988 40 60 modification modification NOUN iajs-1988 40 61             SPACE iajs-1988 40 62 160 160 NUM iajs-1988 40 63     SPACE iajs-1988 40 64 ibn ibn PROPN iajs-1988 40 65 al al PROPN iajs-1988 40 66 - - PUNCT iajs-1988 40 67 haitham haitham PROPN iajs-1988 40 68 jour jour X iajs-1988 40 69 . . PROPN iajs-1988 41 1 for for ADP iajs-1988 41 2 pure pure ADJ iajs-1988 41 3 & & CCONJ iajs-1988 41 4 appl.sci appl.sci PROPN iajs-1988 41 5 . . PUNCT iajs-1988 42 1 ihjpas ihjpas PROPN iajs-1988 42 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 42 3 vol vol NOUN iajs-1988 42 4 . . PUNCT iajs-1988 43 1 32 32 NUM iajs-1988 43 2 ( ( PUNCT iajs-1988 43 3 1 1 NUM iajs-1988 43 4 ) ) PUNCT iajs-1988 43 5 2019 2019 NUM iajs-1988 43 6 theorem theorem VERB iajs-1988 43 7 8 8 NUM iajs-1988 43 8 let let VERB iajs-1988 43 9 𝑋 𝑋 PROPN iajs-1988 43 10 , , PUNCT iajs-1988 43 11 𝒢 𝒢 PROPN iajs-1988 43 12 , , PUNCT iajs-1988 43 13 be be AUX iajs-1988 43 14 a a DET iajs-1988 43 15 partiallyiordered partiallyiordere VERB iajs-1988 43 16 generalized generalized ADJ iajs-1988 43 17 metric metric ADJ iajs-1988 43 18 space space NOUN iajs-1988 43 19 , , PUNCT iajs-1988 43 20 𝒯 𝒯 PROPN iajs-1988 43 21 : : PUNCT iajs-1988 43 22 𝑋 𝑋 PROPN iajs-1988 43 23 → → SYM iajs-1988 43 24 𝑋 𝑋 PROPN iajs-1988 43 25 and and CCONJ iajs-1988 43 26 𝒯 𝒯 PROPN iajs-1988 43 27 , , PUNCT iajs-1988 43 28 𝒯 𝒯 PROPN iajs-1988 43 29 , , PUNCT iajs-1988 43 30 … … PUNCT iajs-1988 43 31 , , PUNCT iajs-1988 43 32 𝒯 𝒯 PROPN iajs-1988 43 33 , , PUNCT iajs-1988 43 34 𝒰 𝒰 PROPN iajs-1988 43 35 and and CCONJ iajs-1988 43 36 𝒱 𝒱 PROPN iajs-1988 43 37 ∶ ∶ NOUN iajs-1988 43 38 𝑋 𝑋 NOUN iajs-1988 43 39 → → SYM iajs-1988 43 40 𝑋 𝑋 PROPN iajs-1988 43 41 are be AUX iajs-1988 43 42 mappingsilies mappingsilie NOUN iajs-1988 43 43 in in ADP iajs-1988 43 44 𝒜 𝒜 NOUN iajs-1988 43 45 and and CCONJ iajs-1988 43 46 hold hold VERB iajs-1988 43 47 that that SCONJ iajs-1988 43 48 following follow VERB iajs-1988 43 49 conditions condition NOUN iajs-1988 43 50 , , PUNCT iajs-1988 43 51 ∀ ∀ X iajs-1988 43 52 𝑥 𝑥 NOUN iajs-1988 43 53 , , PUNCT iajs-1988 43 54 𝑥 𝑥 X iajs-1988 43 55 , , PUNCT iajs-1988 43 56 … … PUNCT iajs-1988 43 57 , , PUNCT iajs-1988 43 58 𝑥 𝑥 X iajs-1988 43 59 , , PUNCT iajs-1988 43 60 𝑦 𝑦 NOUN iajs-1988 43 61 , , PUNCT iajs-1988 43 62 𝑦 𝑦 NOUN iajs-1988 43 63 , , PUNCT iajs-1988 43 64 … … PUNCT iajs-1988 43 65 , , PUNCT iajs-1988 43 66 𝑦 𝑦 NOUN iajs-1988 43 67 ∈ ∈ NOUN iajs-1988 43 68 𝑋 𝑋 NOUN iajs-1988 43 69 𝑎𝑛𝑑 𝑎𝑛𝑑 ADJ iajs-1988 43 70 ℒ ℒ NOUN iajs-1988 43 71 0 0 NUM iajs-1988 44 1 𝒢 𝒢 NOUN iajs-1988 44 2 𝒯 𝒯 PROPN iajs-1988 44 3 𝒯 𝒯 PROPN iajs-1988 44 4 ∗ ∗ NOUN iajs-1988 44 5 … … PUNCT iajs-1988 44 6 ∗ ∗ NOUN iajs-1988 44 7 𝒯 𝒯 PROPN iajs-1988 44 8 𝑥 𝑥 PROPN iajs-1988 44 9 , , PUNCT iajs-1988 44 10 𝑥 𝑥 X iajs-1988 44 11 , , PUNCT iajs-1988 44 12 … … PUNCT iajs-1988 44 13 , , PUNCT iajs-1988 44 14 𝑥 𝑥 INTJ iajs-1988 44 15 , , PUNCT iajs-1988 44 16 𝒯 𝒯 PROPN iajs-1988 44 17 𝒯 𝒯 PROPN iajs-1988 44 18 … … PUNCT iajs-1988 44 19 𝒯 𝒯 PROPN iajs-1988 44 20 𝑦 𝑦 PROPN iajs-1988 44 21 , , PUNCT iajs-1988 44 22 𝑦 𝑦 PRON iajs-1988 44 23 , , PUNCT iajs-1988 44 24 … … PUNCT iajs-1988 44 25 𝑦 𝑦 NOUN iajs-1988 44 26 , , PUNCT iajs-1988 44 27 ℒ ℒ PROPN iajs-1988 44 28 𝓌 𝓌 X iajs-1988 44 29 max max PROPN iajs-1988 44 30 𝜔 𝜔 PROPN iajs-1988 44 31 𝒢 𝒢 PROPN iajs-1988 44 32 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 33 𝑥 𝑥 NOUN iajs-1988 44 34 , , PUNCT iajs-1988 44 35 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 36 𝑦 𝑦 NOUN iajs-1988 44 37 , , PUNCT iajs-1988 44 38 ℒ ℒ NOUN iajs-1988 44 39 , , PUNCT iajs-1988 44 40 𝜔 𝜔 PROPN iajs-1988 44 41 𝒢 𝒢 PROPN iajs-1988 44 42 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 43 𝑥 𝑥 NOUN iajs-1988 44 44 , , PUNCT iajs-1988 44 45 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 46 𝑦 𝑦 NOUN iajs-1988 44 47 , , PUNCT iajs-1988 44 48 ℒ ℒ NOUN iajs-1988 44 49 , , PUNCT iajs-1988 44 50 … … PUNCT iajs-1988 44 51 , , PUNCT iajs-1988 44 52 𝜔 𝜔 X iajs-1988 44 53 𝒢 𝒢 PROPN iajs-1988 44 54 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 55 𝑥 𝑥 NOUN iajs-1988 44 56 , , PUNCT iajs-1988 44 57 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 44 58 𝑦 𝑦 NOUN iajs-1988 44 59 , , PUNCT iajs-1988 44 60 ℒ ℒ PROPN iajs-1988 44 61 1 1 NUM iajs-1988 44 62 where where SCONJ iajs-1988 44 63 is be AUX iajs-1988 44 64 𝓌 𝓌 DET iajs-1988 44 65 upper upper ADJ iajs-1988 44 66 semicontinuous semicontinuous NOUN iajs-1988 44 67 from from ADP iajs-1988 44 68 𝑅 𝑅 PROPN iajs-1988 44 69 into into ADP iajs-1988 44 70 itself itself PRON iajs-1988 44 71 satisfying satisfy VERB iajs-1988 44 72 𝓌 𝓌 X iajs-1988 44 73 𝑥 𝑥 X iajs-1988 44 74 𝑥 𝑥 NOUN iajs-1988 44 75 for for ADP iajs-1988 44 76 all all PRON iajs-1988 44 77 𝑥 𝑥 DET iajs-1988 44 78 0 0 NUM iajs-1988 44 79 .if .if PUNCT iajs-1988 45 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 45 2 𝑥 𝑥 PROPN iajs-1988 45 3 𝒯 𝒯 PROPN iajs-1988 45 4 𝒯 𝒯 PROPN iajs-1988 45 5 … … PUNCT iajs-1988 45 6 𝒯 𝒯 PROPN iajs-1988 45 7 𝑥 𝑥 PROPN iajs-1988 45 8 , , PUNCT iajs-1988 45 9 𝑥 𝑥 X iajs-1988 45 10 , , PUNCT iajs-1988 45 11 … … PUNCT iajs-1988 45 12 … … PUNCT iajs-1988 45 13 , , PUNCT iajs-1988 45 14 𝑥 𝑥 DET iajs-1988 45 15 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 45 16 𝑥 𝑥 PROPN iajs-1988 45 17 𝒯 𝒯 PROPN iajs-1988 45 18 𝒯 𝒯 PROPN iajs-1988 45 19 … … PUNCT iajs-1988 45 20 𝒯 𝒯 PROPN iajs-1988 45 21 𝑥 𝑥 PROPN iajs-1988 45 22 , , PUNCT iajs-1988 45 23 𝑥 𝑥 X iajs-1988 45 24 , , PUNCT iajs-1988 45 25 … … PUNCT iajs-1988 45 26 … … PUNCT iajs-1988 45 27 , , PUNCT iajs-1988 45 28 𝑥 𝑥 X iajs-1988 45 29 , , PUNCT iajs-1988 45 30 𝑥 𝑥 DET iajs-1988 45 31 ⋮ ⋮ NOUN iajs-1988 45 32 2 2 NUM iajs-1988 45 33 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 46 1 𝑥 𝑥 PROPN iajs-1988 46 2 𝒯 𝒯 PROPN iajs-1988 46 3 𝒯 𝒯 PROPN iajs-1988 46 4 … … PUNCT iajs-1988 46 5 𝒯 𝒯 PROPN iajs-1988 46 6 𝑥 𝑥 PROPN iajs-1988 46 7 , , PUNCT iajs-1988 46 8 𝑥 𝑥 X iajs-1988 46 9 , , PUNCT iajs-1988 46 10 𝑥 𝑥 X iajs-1988 46 11 , , PUNCT iajs-1988 46 12 … … PUNCT iajs-1988 46 13 … … PUNCT iajs-1988 46 14 , , PUNCT iajs-1988 46 15 𝑥 𝑥 X iajs-1988 46 16 if if SCONJ iajs-1988 46 17 𝑛 𝑛 PRON iajs-1988 46 18 𝑖𝑠 𝑖𝑠 NOUN iajs-1988 46 19 𝑜𝑑𝑑 𝑜𝑑𝑑 PROPN iajs-1988 46 20 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 47 1 𝑥 𝑥 PROPN iajs-1988 47 2 𝒯 𝒯 PROPN iajs-1988 47 3 𝒯 𝒯 PROPN iajs-1988 47 4 … … PUNCT iajs-1988 47 5 𝒯 𝒯 PROPN iajs-1988 47 6 𝑥 𝑥 PROPN iajs-1988 47 7 , , PUNCT iajs-1988 47 8 𝑥 𝑥 X iajs-1988 47 9 , , PUNCT iajs-1988 47 10 𝑥 𝑥 X iajs-1988 47 11 , , PUNCT iajs-1988 47 12 … … PUNCT iajs-1988 47 13 … … PUNCT iajs-1988 47 14 , , PUNCT iajs-1988 47 15 𝑥 𝑥 X iajs-1988 47 16 if if SCONJ iajs-1988 47 17 𝑛 𝑛 ADJ iajs-1988 48 1 𝑖𝑠 𝑖𝑠 INTJ iajs-1988 48 2 𝑒𝑣𝑒𝑛 𝑒𝑣𝑒𝑛 NOUN iajs-1988 49 1 then then ADV iajs-1988 49 2 𝒯 𝒯 PROPN iajs-1988 49 3 , , PUNCT iajs-1988 49 4 𝒯 𝒯 PROPN iajs-1988 49 5 , , PUNCT iajs-1988 49 6 … … PUNCT iajs-1988 49 7 , , PUNCT iajs-1988 49 8 𝒯 𝒯 PROPN iajs-1988 49 9 , , PUNCT iajs-1988 49 10 𝒰 𝒰 PROPN iajs-1988 50 1 𝑎𝑛𝑑𝒱 𝑎𝑛𝑑𝒱 NOUN iajs-1988 50 2 have have VERB iajs-1988 50 3 a a DET iajs-1988 50 4 modified modify VERB iajs-1988 50 5 tupled tuple VERB iajs-1988 50 6 coincidence coincidence NOUN iajs-1988 50 7 point point NOUN iajs-1988 50 8 . . PUNCT iajs-1988 51 1 proof proof NOUN iajs-1988 51 2 define define VERB iajs-1988 51 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 51 4 𝑥 𝑥 PROPN iajs-1988 51 5 𝒯 𝒯 PROPN iajs-1988 51 6 𝒯 𝒯 PROPN iajs-1988 51 7 … … PUNCT iajs-1988 51 8 𝒯 𝒯 PROPN iajs-1988 51 9 𝑥 𝑥 PROPN iajs-1988 51 10 , , PUNCT iajs-1988 51 11 𝑥 𝑥 X iajs-1988 51 12 , , PUNCT iajs-1988 51 13 … … PUNCT iajs-1988 51 14 … … PUNCT iajs-1988 51 15 , , PUNCT iajs-1988 51 16 𝑥 𝑥 DET iajs-1988 51 17 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 51 18 𝑥 𝑥 PROPN iajs-1988 51 19 𝒯 𝒯 PROPN iajs-1988 51 20 𝒯 𝒯 PROPN iajs-1988 51 21 … … PUNCT iajs-1988 51 22 𝒯 𝒯 PROPN iajs-1988 51 23 𝑥 𝑥 PROPN iajs-1988 51 24 , , PUNCT iajs-1988 51 25 𝑥 𝑥 X iajs-1988 51 26 , , PUNCT iajs-1988 51 27 … … PUNCT iajs-1988 51 28 … … PUNCT iajs-1988 51 29 , , PUNCT iajs-1988 51 30 𝑥 𝑥 X iajs-1988 51 31 , , PUNCT iajs-1988 51 32 𝑥 𝑥 PROPN iajs-1988 51 33 ⋮ ⋮ NOUN iajs-1988 51 34 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 52 1 𝑥 𝑥 PROPN iajs-1988 52 2 𝒯 𝒯 PROPN iajs-1988 52 3 𝒯 𝒯 PROPN iajs-1988 52 4 … … PUNCT iajs-1988 52 5 𝒯 𝒯 PROPN iajs-1988 52 6 𝑥 𝑥 PROPN iajs-1988 52 7 , , PUNCT iajs-1988 52 8 𝑥 𝑥 X iajs-1988 52 9 , , PUNCT iajs-1988 52 10 𝑥 𝑥 X iajs-1988 52 11 , , PUNCT iajs-1988 52 12 … … PUNCT iajs-1988 52 13 … … PUNCT iajs-1988 52 14 , , PUNCT iajs-1988 52 15 𝑥 𝑥 NOUN iajs-1988 52 16 ⟹ ⟹ X iajs-1988 52 17 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 52 18 𝑥 𝑥 INTJ iajs-1988 52 19 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 52 20 𝑥 𝑥 DET iajs-1988 52 21 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 52 22 𝑥 𝑥 DET iajs-1988 52 23 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 52 24 𝑥 𝑥 PROPN iajs-1988 52 25 ⋮ ⋮ NOUN iajs-1988 52 26 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 53 1 𝑥 𝑥 INTJ iajs-1988 54 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 55 1 𝑥 𝑥 NOUN iajs-1988 55 2 if if SCONJ iajs-1988 55 3 𝑛 𝑛 PROPN iajs-1988 55 4 is be AUX iajs-1988 55 5 odd odd ADJ iajs-1988 55 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 55 7 𝑥 𝑥 DET iajs-1988 55 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 56 1 𝑥 𝑥 NOUN iajs-1988 56 2 if if SCONJ iajs-1988 56 3 𝑛 𝑛 PROPN iajs-1988 56 4 is be AUX iajs-1988 56 5 even even ADV iajs-1988 56 6 also also ADV iajs-1988 56 7 , , PUNCT iajs-1988 56 8 we we PRON iajs-1988 56 9 define define VERB iajs-1988 56 10 , , PUNCT iajs-1988 56 11 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 56 12 𝑥 𝑥 PROPN iajs-1988 56 13 𝒯 𝒯 PROPN iajs-1988 56 14 𝒯 𝒯 PROPN iajs-1988 56 15 … … PUNCT iajs-1988 56 16 𝒯 𝒯 PROPN iajs-1988 56 17 𝑥 𝑥 PROPN iajs-1988 56 18 , , PUNCT iajs-1988 56 19 𝑥 𝑥 X iajs-1988 56 20 , , PUNCT iajs-1988 56 21 … … PUNCT iajs-1988 56 22 … … PUNCT iajs-1988 56 23 , , PUNCT iajs-1988 56 24 𝑥 𝑥 DET iajs-1988 56 25 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 57 1 𝑥 𝑥 PROPN iajs-1988 57 2 𝒯 𝒯 PROPN iajs-1988 57 3 𝒯 𝒯 PROPN iajs-1988 57 4 … … PUNCT iajs-1988 57 5 𝒯 𝒯 PROPN iajs-1988 57 6 𝑥 𝑥 PROPN iajs-1988 57 7 , , PUNCT iajs-1988 57 8 𝑥 𝑥 X iajs-1988 57 9 , , PUNCT iajs-1988 57 10 … … PUNCT iajs-1988 57 11 … … PUNCT iajs-1988 57 12 , , PUNCT iajs-1988 57 13 𝑥 𝑥 X iajs-1988 57 14 , , PUNCT iajs-1988 57 15 𝑥 𝑥 DET iajs-1988 57 16 ⋮ ⋮ NOUN iajs-1988 57 17             SPACE iajs-1988 57 18 161 161 NUM iajs-1988 57 19     SPACE iajs-1988 57 20 ibn ibn PROPN iajs-1988 57 21 al al PROPN iajs-1988 57 22 - - PUNCT iajs-1988 57 23 haitham haitham PROPN iajs-1988 57 24 jour jour X iajs-1988 57 25 . . PROPN iajs-1988 58 1 for for ADP iajs-1988 58 2 pure pure ADJ iajs-1988 58 3 & & CCONJ iajs-1988 58 4 appl.sci appl.sci PROPN iajs-1988 58 5 . . PUNCT iajs-1988 59 1 ihjpas ihjpas PROPN iajs-1988 59 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 59 3 vol vol NOUN iajs-1988 59 4 . . PUNCT iajs-1988 60 1 32 32 NUM iajs-1988 60 2 ( ( PUNCT iajs-1988 60 3 1 1 NUM iajs-1988 60 4 ) ) PUNCT iajs-1988 60 5 2019 2019 NUM iajs-1988 60 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 7 𝑥 𝑥 PROPN iajs-1988 60 8 𝒯 𝒯 PROPN iajs-1988 60 9 𝒯 𝒯 PROPN iajs-1988 60 10 … … PUNCT iajs-1988 60 11 𝒯 𝒯 PROPN iajs-1988 60 12 𝑥 𝑥 PROPN iajs-1988 60 13 , , PUNCT iajs-1988 60 14 𝑥 𝑥 X iajs-1988 60 15 , , PUNCT iajs-1988 60 16 … … PUNCT iajs-1988 60 17 … … PUNCT iajs-1988 60 18 , , PUNCT iajs-1988 60 19 𝑥 𝑥 X iajs-1988 60 20 since since SCONJ iajs-1988 60 21 𝑓 𝑓 PRON iajs-1988 60 22 has have VERB iajs-1988 60 23 mixed mixed ADJ iajs-1988 60 24 finite finite ADJ iajs-1988 60 25 monotone monotone ADJ iajs-1988 60 26 property property NOUN iajs-1988 60 27 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 28 𝑥 𝑥 DET iajs-1988 60 29 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 30 𝑥 𝑥 DET iajs-1988 60 31 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 32 𝑥 𝑥 DET iajs-1988 60 33 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 34 𝑥 𝑥 DET iajs-1988 60 35 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 36 𝑥 𝑥 DET iajs-1988 60 37 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 38 𝑥 𝑥 PROPN iajs-1988 60 39 ⋮ ⋮ NOUN iajs-1988 60 40 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 41 𝑥 𝑥 INTJ iajs-1988 60 42 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 60 43 𝑥 𝑥 INTJ iajs-1988 60 44 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 61 1 𝑥 𝑥 NOUN iajs-1988 61 2 if if SCONJ iajs-1988 61 3 𝑛 𝑛 PROPN iajs-1988 61 4 is be AUX iajs-1988 61 5 odd odd ADJ iajs-1988 61 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 61 7 𝑥 𝑥 DET iajs-1988 61 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 61 9 𝑥 𝑥 INTJ iajs-1988 61 10 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 62 1 𝑥 𝑥 NOUN iajs-1988 62 2 if if SCONJ iajs-1988 62 3 𝑛 𝑛 PROPN iajs-1988 62 4 is be AUX iajs-1988 62 5 even even ADV iajs-1988 62 6 continue continue VERB iajs-1988 62 7 process process NOUN iajs-1988 62 8 until until SCONJ iajs-1988 62 9 we we PRON iajs-1988 62 10 get get VERB iajs-1988 62 11 to to ADP iajs-1988 62 12 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 62 13 𝑥 𝑥 DET iajs-1988 62 14 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 62 15 𝑥 𝑥 PROPN iajs-1988 62 16 . . PUNCT iajs-1988 62 17 … … PUNCT iajs-1988 62 18 . . PUNCT iajs-1988 62 19 . . PUNCT iajs-1988 63 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 63 2 𝑥 𝑥 DET iajs-1988 63 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 64 1 𝑥 𝑥 PRON iajs-1988 64 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 64 3 𝑥 𝑥 PROPN iajs-1988 64 4 . . PUNCT iajs-1988 64 5 … … PUNCT iajs-1988 64 6 . . PUNCT iajs-1988 64 7 . . PUNCT iajs-1988 65 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 65 2 𝑥 𝑥 PRON iajs-1988 65 3 ⋮ ⋮ NOUN iajs-1988 65 4 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 65 5 𝑥 𝑥 INTJ iajs-1988 65 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 65 7 𝑥 𝑥 PROPN iajs-1988 65 8 . . PUNCT iajs-1988 65 9 … … PUNCT iajs-1988 65 10 . . PUNCT iajs-1988 65 11 . . PUNCT iajs-1988 66 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 66 2 𝑥 𝑥 NOUN iajs-1988 67 1 if if SCONJ iajs-1988 67 2 𝑛 𝑛 PROPN iajs-1988 67 3 is be AUX iajs-1988 67 4 odd odd ADJ iajs-1988 67 5 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 67 6 𝑥 𝑥 PRON iajs-1988 67 7 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 67 8 𝑥 𝑥 PROPN iajs-1988 67 9 . . PUNCT iajs-1988 68 1 … … PUNCT iajs-1988 68 2 . . PUNCT iajs-1988 68 3 . . PUNCT iajs-1988 69 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 69 2 𝑥 𝑥 NOUN iajs-1988 70 1 if if SCONJ iajs-1988 70 2 𝑛 𝑛 PROPN iajs-1988 70 3 is be AUX iajs-1988 70 4 even even ADV iajs-1988 70 5 in in ADP iajs-1988 70 6 general general ADJ iajs-1988 70 7 : : PUNCT iajs-1988 70 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 70 9 𝑥 𝑥 PROPN iajs-1988 70 10 𝒯 𝒯 PROPN iajs-1988 70 11 𝒯 𝒯 PROPN iajs-1988 70 12 … … PUNCT iajs-1988 70 13 𝒯 𝒯 PROPN iajs-1988 70 14 𝑥 𝑥 PROPN iajs-1988 70 15 , , PUNCT iajs-1988 70 16 𝑥 𝑥 X iajs-1988 70 17 , , PUNCT iajs-1988 70 18 … … PUNCT iajs-1988 70 19 … … PUNCT iajs-1988 70 20 , , PUNCT iajs-1988 70 21 𝑥 𝑥 DET iajs-1988 70 22 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 71 1 𝑥 𝑥 PROPN iajs-1988 71 2 𝒯 𝒯 PROPN iajs-1988 71 3 𝒯 𝒯 PROPN iajs-1988 71 4 … … PUNCT iajs-1988 71 5 𝒯 𝒯 PROPN iajs-1988 71 6 𝑥 𝑥 PROPN iajs-1988 71 7 , , PUNCT iajs-1988 71 8 𝑥 𝑥 X iajs-1988 71 9 , , PUNCT iajs-1988 71 10 … … PUNCT iajs-1988 71 11 … … PUNCT iajs-1988 71 12 , , PUNCT iajs-1988 71 13 𝑥 𝑥 X iajs-1988 71 14 , , PUNCT iajs-1988 71 15 𝑥 𝑥 PROPN iajs-1988 71 16 ⋮ ⋮ NOUN iajs-1988 71 17 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 72 1 𝑥 𝑥 PROPN iajs-1988 72 2 𝒯 𝒯 PROPN iajs-1988 72 3 𝒯 𝒯 PROPN iajs-1988 72 4 … … PUNCT iajs-1988 72 5 𝒯 𝒯 PROPN iajs-1988 72 6 𝑥 𝑥 PROPN iajs-1988 72 7 , , PUNCT iajs-1988 72 8 𝑥 𝑥 X iajs-1988 72 9 , , PUNCT iajs-1988 72 10 𝑥 𝑥 X iajs-1988 72 11 , , PUNCT iajs-1988 72 12 … … PUNCT iajs-1988 72 13 … … PUNCT iajs-1988 72 14 , , PUNCT iajs-1988 72 15 𝑥 𝑥 PROPN iajs-1988 72 16 and and CCONJ iajs-1988 72 17 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 72 18 𝑥 𝑥 DET iajs-1988 72 19 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 72 20 𝑥 𝑥 PROPN iajs-1988 72 21 . . PUNCT iajs-1988 72 22 … … PUNCT iajs-1988 72 23 . . PUNCT iajs-1988 72 24 . . PUNCT iajs-1988 73 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 73 2 𝑥 𝑥 DET iajs-1988 73 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 74 1 𝑥 𝑥 PROPN iajs-1988 74 2 . . PUNCT iajs-1988 75 1 … … PUNCT iajs-1988 75 2 … … PUNCT iajs-1988 75 3 .. .. PUNCT iajs-1988 76 1 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 77 1 𝑥 𝑥 DET iajs-1988 77 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 77 3 𝑥 𝑥 PROPN iajs-1988 77 4 . . PUNCT iajs-1988 77 5 … … PUNCT iajs-1988 77 6 . . PUNCT iajs-1988 77 7 . . PUNCT iajs-1988 78 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 78 2 𝑥 𝑥 DET iajs-1988 78 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 79 1 𝑥 𝑥 PROPN iajs-1988 79 2 . . PUNCT iajs-1988 80 1 … … PUNCT iajs-1988 80 2 … … PUNCT iajs-1988 80 3 .. .. PUNCT iajs-1988 80 4 ⋮ ⋮ NOUN iajs-1988 80 5 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 81 1 𝑥 𝑥 PRON iajs-1988 81 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 81 3 𝑥 𝑥 PROPN iajs-1988 81 4 . . PUNCT iajs-1988 82 1 … … PUNCT iajs-1988 82 2 . . PUNCT iajs-1988 82 3 . . PUNCT iajs-1988 83 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 83 2 𝑥 𝑥 DET iajs-1988 83 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 84 1 𝑥 𝑥 PROPN iajs-1988 84 2 . . PUNCT iajs-1988 85 1 … … PUNCT iajs-1988 85 2 .. .. PUNCT iajs-1988 86 1 if if SCONJ iajs-1988 86 2 𝑛 𝑛 PROPN iajs-1988 86 3 is be AUX iajs-1988 86 4 odd odd ADJ iajs-1988 86 5 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 86 6 𝑥 𝑥 PRON iajs-1988 86 7 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 86 8 𝑥 𝑥 PROPN iajs-1988 86 9 . . PUNCT iajs-1988 86 10 … … PUNCT iajs-1988 86 11 . . PUNCT iajs-1988 86 12 . . PUNCT iajs-1988 87 1 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 87 2 𝑥 𝑥 DET iajs-1988 87 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 88 1 𝑥 𝑥 PROPN iajs-1988 88 2 . . PUNCT iajs-1988 89 1 … … PUNCT iajs-1988 89 2 .. .. PUNCT iajs-1988 90 1 if if SCONJ iajs-1988 90 2 𝑛 𝑛 PRON iajs-1988 90 3 is be AUX iajs-1988 90 4 even even ADV iajs-1988 90 5 now now ADV iajs-1988 90 6 , , PUNCT iajs-1988 90 7 we we PRON iajs-1988 90 8 have have VERB iajs-1988 90 9 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 10 𝑥 𝑥 NOUN iajs-1988 90 11 , , PUNCT iajs-1988 90 12 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 13 𝑥 𝑥 X iajs-1988 90 14 , , PUNCT iajs-1988 90 15 … … PUNCT iajs-1988 90 16 … … PUNCT iajs-1988 90 17 𝑎𝑛𝑑 𝑎𝑛𝑑 ADJ iajs-1988 90 18 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 19 𝑥 𝑥 PROPN iajs-1988 90 20 are be AUX iajs-1988 90 21 sequence sequence NOUN iajs-1988 90 22 in in ADP iajs-1988 90 23 𝑔𝑇 𝑔𝑇 NOUN iajs-1988 90 24 𝑋 𝑋 PROPN iajs-1988 90 25 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 26 𝑥 𝑥 NOUN iajs-1988 90 27 → → SYM iajs-1988 90 28 𝑟 𝑟 NOUN iajs-1988 90 29 , , PUNCT iajs-1988 90 30 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 31 𝑥 𝑥 X iajs-1988 90 32 → → SYM iajs-1988 90 33 𝑟 𝑟 NOUN iajs-1988 90 34 , , PUNCT iajs-1988 90 35 … … PUNCT iajs-1988 90 36 … … PUNCT iajs-1988 90 37 … … PUNCT iajs-1988 90 38 , , PUNCT iajs-1988 90 39 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 90 40 𝑥 𝑥 X iajs-1988 90 41 → → SYM iajs-1988 90 42 𝑟 𝑟 NOUN iajs-1988 90 43             SPACE iajs-1988 90 44 162 162 NUM iajs-1988 90 45     SPACE iajs-1988 90 46 ibn ibn PROPN iajs-1988 90 47 al al PROPN iajs-1988 90 48 - - PUNCT iajs-1988 90 49 haitham haitham PROPN iajs-1988 90 50 jour jour X iajs-1988 90 51 . . PROPN iajs-1988 91 1 for for ADP iajs-1988 91 2 pure pure ADJ iajs-1988 91 3 & & CCONJ iajs-1988 91 4 appl.sci appl.sci PROPN iajs-1988 91 5 . . PUNCT iajs-1988 92 1 ihjpas ihjpas PROPN iajs-1988 92 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 92 3 vol vol NOUN iajs-1988 92 4 . . PUNCT iajs-1988 93 1 32 32 NUM iajs-1988 93 2 ( ( PUNCT iajs-1988 93 3 1 1 NUM iajs-1988 93 4 ) ) PUNCT iajs-1988 93 5 2019 2019 NUM iajs-1988 93 6 since since SCONJ iajs-1988 93 7 𝑟 𝑟 NOUN iajs-1988 93 8 , , PUNCT iajs-1988 93 9 𝑟 𝑟 X iajs-1988 93 10 , , PUNCT iajs-1988 93 11 … … PUNCT iajs-1988 93 12 … … PUNCT iajs-1988 93 13 , , PUNCT iajs-1988 93 14 𝑟 𝑟 X iajs-1988 93 15 ∈ ∈ PROPN iajs-1988 93 16 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 93 17 𝑋 𝑋 PROPN iajs-1988 93 18 , , PUNCT iajs-1988 93 19 then then ADV iajs-1988 93 20 there there PRON iajs-1988 93 21 exists exist VERB iajs-1988 93 22 𝑥 𝑥 PRON iajs-1988 93 23 , , PUNCT iajs-1988 93 24 𝑥 𝑥 X iajs-1988 93 25 , , PUNCT iajs-1988 93 26 … … PUNCT iajs-1988 93 27 … … PUNCT iajs-1988 93 28 , , PUNCT iajs-1988 93 29 𝑥 𝑥 PROPN iajs-1988 93 30 ∈ ∈ PROPN iajs-1988 93 31 𝑋. 𝑋. PROPN iajs-1988 93 32 such such ADJ iajs-1988 93 33 that that SCONJ iajs-1988 93 34 , , PUNCT iajs-1988 93 35 𝑟 𝑟 X iajs-1988 93 36 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 93 37 𝑥 𝑥 X iajs-1988 93 38 , , PUNCT iajs-1988 93 39 𝑟 𝑟 X iajs-1988 93 40 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 93 41 𝑥 𝑥 X iajs-1988 93 42 , , PUNCT iajs-1988 93 43 … … PUNCT iajs-1988 93 44 … … PUNCT iajs-1988 93 45 . . PUNCT iajs-1988 94 1 , , PUNCT iajs-1988 94 2 𝑟 𝑟 X iajs-1988 94 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 94 4 𝑥 𝑥 VERB iajs-1988 94 5 considering consider VERB iajs-1988 94 6 the the DET iajs-1988 94 7 hypotheses hypothesis NOUN iajs-1988 94 8 ( ( PUNCT iajs-1988 94 9 i i NOUN iajs-1988 94 10 ) ) PUNCT iajs-1988 94 11 and and CCONJ iajs-1988 94 12 ( ( PUNCT iajs-1988 94 13 ii ii NOUN iajs-1988 94 14 ) ) PUNCT iajs-1988 94 15 give give VERB iajs-1988 94 16 in in ADP iajs-1988 94 17 the the DET iajs-1988 94 18 theorem theorem NOUN iajs-1988 94 19 we we PRON iajs-1988 94 20 get get VERB iajs-1988 94 21 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 94 22 𝑥 𝑥 DET iajs-1988 94 23 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 94 24 𝑥 𝑥 X iajs-1988 94 25 𝑟 𝑟 PUNCT iajs-1988 94 26 𝒰𝒱 𝒰𝒱 ADJ iajs-1988 94 27 𝑥 𝑥 PRON iajs-1988 94 28 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 94 29 𝑥 𝑥 PROPN iajs-1988 94 30 𝑟 𝑟 NOUN iajs-1988 94 31 ⋮ ⋮ ADJ iajs-1988 94 32 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 94 33 𝑥 𝑥 INTJ iajs-1988 94 34 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 94 35 𝑥 𝑥 NOUN iajs-1988 95 1 𝑟 𝑟 NOUN iajs-1988 95 2 𝑖𝑓 𝑖𝑓 ADP iajs-1988 95 3 𝑛 𝑛 DET iajs-1988 95 4 𝑖𝑠 𝑖𝑠 NOUN iajs-1988 95 5 𝑜𝑑𝑑 𝑜𝑑𝑑 PROPN iajs-1988 95 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 7 𝑥 𝑥 INTJ iajs-1988 95 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 9 𝑥 𝑥 NOUN iajs-1988 95 10 𝑟 𝑟 NOUN iajs-1988 95 11 𝑖𝑓 𝑖𝑓 NOUN iajs-1988 95 12 𝑛 𝑛 PRON iajs-1988 95 13 𝑖𝑠 𝑖𝑠 INTJ iajs-1988 95 14 𝑒𝑣𝑒𝑛 𝑒𝑣𝑒𝑛 ADJ iajs-1988 95 15 since since SCONJ iajs-1988 95 16 𝒰 𝒰 PROPN iajs-1988 95 17 and and CCONJ iajs-1988 95 18 𝒱 𝒱 PROPN iajs-1988 95 19 are be AUX iajs-1988 95 20 continuous continuous ADJ iajs-1988 95 21 mapping mapping NOUN iajs-1988 95 22 , , PUNCT iajs-1988 95 23 then then ADV iajs-1988 95 24 we we PRON iajs-1988 95 25 have have VERB iajs-1988 95 26 : : PUNCT iajs-1988 95 27 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 28 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 29 𝑥 𝑥 PROPN iajs-1988 95 30 → → SYM iajs-1988 95 31 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 32 𝑟 𝑟 SYM iajs-1988 95 33 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 34 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 35 𝑥 𝑥 PROPN iajs-1988 95 36 → → SYM iajs-1988 95 37 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 38 𝑟 𝑟 NOUN iajs-1988 95 39 ⋮ ⋮ NOUN iajs-1988 95 40 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 95 41 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 96 1 𝑥 𝑥 PROPN iajs-1988 96 2 → → SYM iajs-1988 96 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 96 4 𝑟 𝑟 NOUN iajs-1988 96 5 and and CCONJ iajs-1988 96 6 hence hence ADV iajs-1988 96 7 , , PUNCT iajs-1988 96 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 96 9 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 96 10 𝑥 𝑥 DET iajs-1988 96 11 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 97 1 𝑟 𝑟 PRON iajs-1988 97 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 97 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 1 𝑥 𝑥 PRON iajs-1988 98 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 3 𝑟 𝑟 NOUN iajs-1988 98 4 ⋮ ⋮ NOUN iajs-1988 98 5 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 7 𝑥 𝑥 DET iajs-1988 98 8 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 9 𝑟 𝑟 NOUN iajs-1988 98 10 𝑖𝑓 𝑖𝑓 ADP iajs-1988 98 11 𝑛 𝑛 DET iajs-1988 98 12 𝑖𝑠 𝑖𝑠 NOUN iajs-1988 98 13 𝑜𝑑𝑑 𝑜𝑑𝑑 PROPN iajs-1988 98 14 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 15 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 16 𝑥 𝑥 DET iajs-1988 98 17 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 18 𝑟 𝑟 NOUN iajs-1988 98 19 𝑖𝑓 𝑖𝑓 ADP iajs-1988 98 20 𝑛 𝑛 DET iajs-1988 98 21 𝑖𝑠 𝑖𝑠 INTJ iajs-1988 98 22 𝑒𝑣𝑒𝑛 𝑒𝑣𝑒𝑛 ADJ iajs-1988 98 23 choose choose VERB iajs-1988 98 24 ℒ ℒ NOUN iajs-1988 98 25 satisfy satisfy NOUN iajs-1988 98 26 : : PUNCT iajs-1988 98 27 𝒢 𝒢 PROPN iajs-1988 98 28 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 29 𝑟 𝑟 X iajs-1988 98 30 , , PUNCT iajs-1988 98 31 𝒯 𝒯 PROPN iajs-1988 98 32 𝒯 𝒯 PROPN iajs-1988 98 33 … … PUNCT iajs-1988 98 34 𝒯 𝒯 PROPN iajs-1988 98 35 𝑟 𝑟 NOUN iajs-1988 98 36 , , PUNCT iajs-1988 98 37 𝑟 𝑟 X iajs-1988 98 38 , , PUNCT iajs-1988 98 39 … … PUNCT iajs-1988 98 40 … … PUNCT iajs-1988 98 41 , , PUNCT iajs-1988 98 42 𝑟 𝑟 X iajs-1988 98 43 , , PUNCT iajs-1988 98 44 ℒ ℒ PROPN iajs-1988 98 45 𝒢 𝒢 PROPN iajs-1988 98 46 𝒯 𝒯 PROPN iajs-1988 98 47 𝒯 𝒯 PROPN iajs-1988 98 48 … … PUNCT iajs-1988 98 49 𝒯 𝒯 PROPN iajs-1988 98 50 𝑟 𝑟 NOUN iajs-1988 98 51 , , PUNCT iajs-1988 98 52 𝑟 𝑟 X iajs-1988 98 53 , , PUNCT iajs-1988 98 54 … … PUNCT iajs-1988 98 55 … … PUNCT iajs-1988 98 56 , , PUNCT iajs-1988 98 57 𝑟 𝑟 X iajs-1988 98 58 , , PUNCT iajs-1988 98 59 ℒ ℒ PROPN iajs-1988 98 60 , , PUNCT iajs-1988 98 61 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 62 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 98 63 𝑥 𝑥 PROPN iajs-1988 99 1 𝒢 𝒢 PROPN iajs-1988 99 2 𝒯 𝒯 PROPN iajs-1988 99 3 𝒯 𝒯 PROPN iajs-1988 99 4 … … PUNCT iajs-1988 99 5 𝒯 𝒯 PROPN iajs-1988 99 6 𝑟 𝑟 NOUN iajs-1988 99 7 , , PUNCT iajs-1988 99 8 𝑟 𝑟 X iajs-1988 99 9 , , PUNCT iajs-1988 99 10 … … PUNCT iajs-1988 99 11 … … PUNCT iajs-1988 99 12 , , PUNCT iajs-1988 99 13 𝑟 𝑟 NOUN iajs-1988 99 14 , , PUNCT iajs-1988 99 15 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 16 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 17 𝑥 𝑥 PROPN iajs-1988 99 18 , , PUNCT iajs-1988 99 19 ℒ ℒ NOUN iajs-1988 99 20 𝒢 𝒢 PROPN iajs-1988 99 21 𝒯 𝒯 PROPN iajs-1988 99 22 𝒯 𝒯 PROPN iajs-1988 99 23 … … PUNCT iajs-1988 99 24 𝒯 𝒯 PROPN iajs-1988 99 25 𝑟 𝑟 NOUN iajs-1988 99 26 , , PUNCT iajs-1988 99 27 𝑟 𝑟 X iajs-1988 99 28 , , PUNCT iajs-1988 99 29 … … PUNCT iajs-1988 99 30 … … PUNCT iajs-1988 99 31 , , PUNCT iajs-1988 99 32 𝑟 𝑟 X iajs-1988 99 33 , , PUNCT iajs-1988 99 34 𝒯 𝒯 PROPN iajs-1988 99 35 𝒯 𝒯 PROPN iajs-1988 99 36 … … PUNCT iajs-1988 99 37 𝒯 𝒯 PROPN iajs-1988 99 38 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 39 𝑥 𝑥 PROPN iajs-1988 99 40 , , PUNCT iajs-1988 99 41 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 42 𝑥 𝑥 X iajs-1988 99 43 , , PUNCT iajs-1988 99 44 … … PUNCT iajs-1988 99 45 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 46 𝑥 𝑥 NOUN iajs-1988 99 47 , , PUNCT iajs-1988 99 48 ℒ ℒ PROPN iajs-1988 99 49 𝓌 𝓌 PRON iajs-1988 99 50 max max PROPN iajs-1988 99 51 𝜔 𝜔 PROPN iajs-1988 99 52 𝒢 𝒢 PROPN iajs-1988 99 53 𝒱 𝒱 PROPN iajs-1988 99 54 𝑟 𝑟 NOUN iajs-1988 99 55 , , PUNCT iajs-1988 99 56 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 57 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 58 𝑥 𝑥 PROPN iajs-1988 99 59 , , PUNCT iajs-1988 99 60 ℒ ℒ NOUN iajs-1988 99 61 , , PUNCT iajs-1988 99 62 𝜔 𝜔 PROPN iajs-1988 99 63 𝒢 𝒢 PROPN iajs-1988 99 64 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 65 𝑟 𝑟 NOUN iajs-1988 99 66 , , PUNCT iajs-1988 99 67 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 68 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 69 𝑥 𝑥 X iajs-1988 99 70 , , PUNCT iajs-1988 99 71 ℒ ℒ NOUN iajs-1988 99 72 , , PUNCT iajs-1988 99 73 … … PUNCT iajs-1988 99 74 , , PUNCT iajs-1988 99 75 𝜔 𝜔 PROPN iajs-1988 99 76 𝒢 𝒢 PROPN iajs-1988 99 77 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 78 𝑟 𝑟 NOUN iajs-1988 99 79 , , PUNCT iajs-1988 99 80 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 81 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 82 𝑥 𝑥 PROPN iajs-1988 99 83 , , PUNCT iajs-1988 99 84 ℒ ℒ PROPN iajs-1988 99 85 𝓌 𝓌 PRON iajs-1988 99 86 max max NOUN iajs-1988 99 87 𝒢 𝒢 PROPN iajs-1988 99 88 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 89 𝑟 𝑟 NOUN iajs-1988 99 90 , , PUNCT iajs-1988 99 91 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 92 𝑥 𝑥 X iajs-1988 99 93 , , PUNCT iajs-1988 99 94 ℒ ℒ NOUN iajs-1988 99 95 , , PUNCT iajs-1988 99 96 𝒢 𝒢 PROPN iajs-1988 99 97 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 98 𝑟 𝑟 NOUN iajs-1988 99 99 , , PUNCT iajs-1988 99 100 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 101 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 102 𝑥 𝑥 X iajs-1988 99 103 , , PUNCT iajs-1988 99 104 ℒ ℒ NOUN iajs-1988 99 105 , , PUNCT iajs-1988 99 106 … … PUNCT iajs-1988 99 107 , , PUNCT iajs-1988 99 108 𝒢 𝒢 PROPN iajs-1988 99 109 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 110 𝑟 𝑟 NOUN iajs-1988 99 111 , , PUNCT iajs-1988 99 112 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 113 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 114 𝑥 𝑥 PROPN iajs-1988 99 115 , , PUNCT iajs-1988 99 116 ℒ ℒ PROPN iajs-1988 99 117 but but CCONJ iajs-1988 99 118 , , PUNCT iajs-1988 99 119 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 120 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 121 𝑥 𝑥 PROPN iajs-1988 99 122 → → SYM iajs-1988 99 123 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 124 𝑟 𝑟 NOUN iajs-1988 99 125 , , PUNCT iajs-1988 99 126 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 127 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 128 𝑥 𝑥 PROPN iajs-1988 99 129 → → SYM iajs-1988 99 130 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 99 131 𝑟 𝑟 NOUN iajs-1988 99 132 , , PUNCT iajs-1988 99 133 … … PUNCT iajs-1988 99 134 … … PUNCT iajs-1988 99 135 … … PUNCT iajs-1988 99 136 .. .. PUNCT iajs-1988 99 137 and and CCONJ iajs-1988 99 138             SPACE iajs-1988 99 139 163 163 NUM iajs-1988 99 140     SPACE iajs-1988 99 141 ibn ibn PROPN iajs-1988 99 142 al al PROPN iajs-1988 99 143 - - PUNCT iajs-1988 99 144 haitham haitham PROPN iajs-1988 99 145 jour jour X iajs-1988 99 146 . . PROPN iajs-1988 100 1 for for ADP iajs-1988 100 2 pure pure ADJ iajs-1988 100 3 & & CCONJ iajs-1988 100 4 appl.sci appl.sci PROPN iajs-1988 100 5 . . PUNCT iajs-1988 101 1 ihjpas ihjpas PROPN iajs-1988 101 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 101 3 vol vol NOUN iajs-1988 101 4 . . PUNCT iajs-1988 102 1 32 32 NUM iajs-1988 102 2 ( ( PUNCT iajs-1988 102 3 1 1 NUM iajs-1988 102 4 ) ) PUNCT iajs-1988 102 5 2019 2019 NUM iajs-1988 102 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 102 7 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 102 8 𝑥 𝑥 PROPN iajs-1988 102 9 → → SYM iajs-1988 102 10 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 102 11 𝑟 𝑟 NOUN iajs-1988 102 12 which which PRON iajs-1988 102 13 is be AUX iajs-1988 102 14 implies imply VERB iajs-1988 102 15 , , PUNCT iajs-1988 102 16 by by ADP iajs-1988 102 17 definition definition NOUN iajs-1988 102 18 𝒢-convergentiin 𝒢-convergentiin PROPN iajs-1988 102 19 𝒢-metric 𝒢-metric PROPN iajs-1988 102 20 space space NOUN iajs-1988 103 1 , , PUNCT iajs-1988 103 2 𝒢 𝒢 PROPN iajs-1988 103 3 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 4 𝑟 𝑟 NOUN iajs-1988 103 5 , , PUNCT iajs-1988 103 6 𝒯 𝒯 PROPN iajs-1988 103 7 𝒯 𝒯 PROPN iajs-1988 103 8 … … PUNCT iajs-1988 103 9 𝒯 𝒯 PROPN iajs-1988 103 10 𝑟 𝑟 NOUN iajs-1988 103 11 , , PUNCT iajs-1988 103 12 𝑟 𝑟 X iajs-1988 103 13 , , PUNCT iajs-1988 103 14 … … PUNCT iajs-1988 103 15 … … PUNCT iajs-1988 103 16 , , PUNCT iajs-1988 103 17 𝑟 𝑟 X iajs-1988 103 18 , , PUNCT iajs-1988 103 19 ℒ ℒ X iajs-1988 103 20 0 0 NUM iajs-1988 103 21 ⟹ ⟹ NUM iajs-1988 103 22 𝒯 𝒯 PROPN iajs-1988 103 23 𝒯 𝒯 PROPN iajs-1988 103 24 … … PUNCT iajs-1988 103 25 𝒯 𝒯 PROPN iajs-1988 103 26 𝑟 𝑟 NOUN iajs-1988 103 27 , , PUNCT iajs-1988 103 28 𝑟 𝑟 X iajs-1988 103 29 , , PUNCT iajs-1988 103 30 … … PUNCT iajs-1988 103 31 … … PUNCT iajs-1988 103 32 , , PUNCT iajs-1988 103 33 𝑟 𝑟 X iajs-1988 103 34 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 103 35 𝑟 𝑟 NOUN iajs-1988 103 36 also also ADV iajs-1988 103 37 , , PUNCT iajs-1988 103 38 choose choose VERB iajs-1988 103 39 ℒ ℒ NOUN iajs-1988 103 40 satisfy satisfy NOUN iajs-1988 103 41 : : PUNCT iajs-1988 103 42 𝒢 𝒢 PROPN iajs-1988 103 43 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 44 𝑟 𝑟 X iajs-1988 103 45 , , PUNCT iajs-1988 103 46 𝒯 𝒯 PROPN iajs-1988 103 47 𝒯 𝒯 PROPN iajs-1988 103 48 … … PUNCT iajs-1988 103 49 𝒯 𝒯 PROPN iajs-1988 103 50 𝑟 𝑟 NOUN iajs-1988 103 51 , , PUNCT iajs-1988 103 52 𝑟 𝑟 X iajs-1988 103 53 , , PUNCT iajs-1988 103 54 … … PUNCT iajs-1988 103 55 , , PUNCT iajs-1988 103 56 𝑟 𝑟 X iajs-1988 103 57 , , PUNCT iajs-1988 103 58 ℒ ℒ PROPN iajs-1988 103 59 𝒢 𝒢 PROPN iajs-1988 103 60 𝒯 𝒯 PROPN iajs-1988 103 61 𝒯 𝒯 PROPN iajs-1988 103 62 … … PUNCT iajs-1988 103 63 𝒯 𝒯 PROPN iajs-1988 103 64 𝑟 𝑟 NOUN iajs-1988 103 65 , , PUNCT iajs-1988 103 66 𝑟 𝑟 X iajs-1988 103 67 , , PUNCT iajs-1988 103 68 … … PUNCT iajs-1988 103 69 , , PUNCT iajs-1988 103 70 𝑟 𝑟 X iajs-1988 103 71 , , PUNCT iajs-1988 103 72 ℒ ℒ NOUN iajs-1988 103 73 , , PUNCT iajs-1988 103 74 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 75 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 76 𝑥 𝑥 PROPN iajs-1988 103 77 𝒢 𝒢 PROPN iajs-1988 103 78 𝒯 𝒯 PROPN iajs-1988 103 79 𝒯 𝒯 PROPN iajs-1988 103 80 … … PUNCT iajs-1988 103 81 𝒯 𝒯 PROPN iajs-1988 103 82 𝑟 𝑟 NOUN iajs-1988 103 83 , , PUNCT iajs-1988 103 84 𝑟 𝑟 X iajs-1988 103 85 , , PUNCT iajs-1988 103 86 … … PUNCT iajs-1988 103 87 , , PUNCT iajs-1988 103 88 𝑟 𝑟 X iajs-1988 103 89 , , PUNCT iajs-1988 103 90 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 91 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 92 𝑥 𝑥 PROPN iajs-1988 103 93 , , PUNCT iajs-1988 103 94 ℒ ℒ NOUN iajs-1988 103 95 𝒢 𝒢 PROPN iajs-1988 103 96 𝒯 𝒯 PROPN iajs-1988 103 97 𝒯 𝒯 PROPN iajs-1988 103 98 … … PUNCT iajs-1988 103 99 𝒯 𝒯 PROPN iajs-1988 103 100 𝑟 𝑟 NOUN iajs-1988 103 101 , , PUNCT iajs-1988 103 102 𝑟 𝑟 X iajs-1988 103 103 , , PUNCT iajs-1988 103 104 … … PUNCT iajs-1988 103 105 , , PUNCT iajs-1988 103 106 𝑟 𝑟 X iajs-1988 103 107 , , PUNCT iajs-1988 103 108 𝒯 𝒯 PROPN iajs-1988 103 109 𝒯 𝒯 PROPN iajs-1988 103 110 … … PUNCT iajs-1988 103 111 𝒯 𝒯 PROPN iajs-1988 103 112 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 113 𝑥 𝑥 PROPN iajs-1988 103 114 , , PUNCT iajs-1988 103 115 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 116 𝑥 𝑥 X iajs-1988 103 117 , , PUNCT iajs-1988 103 118 … … PUNCT iajs-1988 103 119 , , PUNCT iajs-1988 103 120 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 121 𝑥 𝑥 X iajs-1988 103 122 , , PUNCT iajs-1988 103 123 ℒ ℒ PROPN iajs-1988 103 124 𝓌 𝓌 PRON iajs-1988 103 125 max max PROPN iajs-1988 103 126 𝜔 𝜔 PROPN iajs-1988 103 127 𝒢 𝒢 PROPN iajs-1988 103 128 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 129 𝑟 𝑟 NOUN iajs-1988 103 130 , , PUNCT iajs-1988 103 131 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 132 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 133 𝑥 𝑥 PROPN iajs-1988 103 134 , , PUNCT iajs-1988 103 135 ℒ ℒ NOUN iajs-1988 103 136 , , PUNCT iajs-1988 103 137 𝜔 𝜔 PROPN iajs-1988 103 138 𝒢 𝒢 PROPN iajs-1988 103 139 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 140 𝑟 𝑟 NOUN iajs-1988 103 141 , , PUNCT iajs-1988 103 142 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 143 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 144 𝑥 𝑥 X iajs-1988 103 145 , , PUNCT iajs-1988 103 146 ℒ ℒ NOUN iajs-1988 103 147 , , PUNCT iajs-1988 103 148 … … PUNCT iajs-1988 103 149 , , PUNCT iajs-1988 103 150 𝜔 𝜔 PROPN iajs-1988 103 151 𝒢 𝒢 PROPN iajs-1988 103 152 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 153 𝑟 𝑟 NOUN iajs-1988 103 154 , , PUNCT iajs-1988 103 155 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 156 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 157 𝑥 𝑥 PROPN iajs-1988 103 158 , , PUNCT iajs-1988 103 159 ℒ ℒ PROPN iajs-1988 103 160 𝓌 𝓌 PRON iajs-1988 103 161 max max NOUN iajs-1988 103 162 𝒢 𝒢 PROPN iajs-1988 103 163 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 164 𝑟 𝑟 NOUN iajs-1988 103 165 , , PUNCT iajs-1988 103 166 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 167 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 168 𝑥 𝑥 X iajs-1988 103 169 , , PUNCT iajs-1988 103 170 ℒ ℒ NOUN iajs-1988 103 171 , , PUNCT iajs-1988 103 172 𝒢 𝒢 PROPN iajs-1988 103 173 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 174 𝑟 𝑟 NOUN iajs-1988 103 175 , , PUNCT iajs-1988 103 176 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 177 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 178 𝑥 𝑥 X iajs-1988 103 179 , , PUNCT iajs-1988 103 180 ℒ ℒ NOUN iajs-1988 103 181 , , PUNCT iajs-1988 103 182 … … PUNCT iajs-1988 103 183 , , PUNCT iajs-1988 103 184 𝒢 𝒢 PROPN iajs-1988 103 185 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 186 𝑟 𝑟 NOUN iajs-1988 103 187 , , PUNCT iajs-1988 103 188 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 189 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 190 𝑥 𝑥 PROPN iajs-1988 103 191 , , PUNCT iajs-1988 103 192 ℒ ℒ PROPN iajs-1988 103 193 but but CCONJ iajs-1988 103 194 , , PUNCT iajs-1988 103 195 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 196 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 197 𝑥 𝑥 PROPN iajs-1988 103 198 → → SYM iajs-1988 103 199 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 200 𝑟 𝑟 NOUN iajs-1988 103 201 , , PUNCT iajs-1988 103 202 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 203 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 204 𝑥 𝑥 PROPN iajs-1988 103 205 → → SYM iajs-1988 103 206 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 207 𝑟 𝑟 NOUN iajs-1988 103 208 , , PUNCT iajs-1988 103 209 … … PUNCT iajs-1988 103 210 …… …… NOUN iajs-1988 103 211 .. .. PUNCT iajs-1988 103 212 and and CCONJ iajs-1988 103 213 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 214 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 215 𝑥 𝑥 PROPN iajs-1988 103 216 → → SYM iajs-1988 103 217 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 218 𝑟 𝑟 NOUN iajs-1988 103 219 which which PRON iajs-1988 103 220 is be AUX iajs-1988 103 221 implies imply VERB iajs-1988 103 222 , , PUNCT iajs-1988 103 223 by by ADP iajs-1988 103 224 definition definition NOUN iajs-1988 103 225 𝒢 𝒢 NOUN iajs-1988 103 226 -convergent -convergent NOUN iajs-1988 103 227 in in ADP iajs-1988 103 228 𝒢-metric 𝒢-metric ADJ iajs-1988 103 229 space space NOUN iajs-1988 103 230 , , PUNCT iajs-1988 103 231 𝒢 𝒢 PROPN iajs-1988 103 232 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 233 𝑟 𝑟 NOUN iajs-1988 103 234 , , PUNCT iajs-1988 103 235 𝒯 𝒯 PROPN iajs-1988 103 236 𝒯 𝒯 PROPN iajs-1988 103 237 … … PUNCT iajs-1988 103 238 𝒯 𝒯 PROPN iajs-1988 103 239 𝑟 𝑟 NOUN iajs-1988 103 240 , , PUNCT iajs-1988 103 241 𝑟 𝑟 X iajs-1988 103 242 , , PUNCT iajs-1988 103 243 … … PUNCT iajs-1988 103 244 … … PUNCT iajs-1988 103 245 , , PUNCT iajs-1988 103 246 𝑟 𝑟 X iajs-1988 103 247 , , PUNCT iajs-1988 103 248 ℒ ℒ X iajs-1988 103 249 0 0 NUM iajs-1988 103 250 ⟹ ⟹ NUM iajs-1988 103 251 𝒯 𝒯 PROPN iajs-1988 103 252 𝒯 𝒯 PROPN iajs-1988 103 253 … … PUNCT iajs-1988 103 254 𝒯 𝒯 PROPN iajs-1988 103 255 𝑟 𝑟 NOUN iajs-1988 103 256 , , PUNCT iajs-1988 103 257 𝑟 𝑟 X iajs-1988 103 258 , , PUNCT iajs-1988 103 259 … … PUNCT iajs-1988 103 260 … … PUNCT iajs-1988 103 261 , , PUNCT iajs-1988 103 262 𝑟 𝑟 X iajs-1988 103 263 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 103 264 𝑟 𝑟 NOUN iajs-1988 103 265 continue continue VERB iajs-1988 103 266 these these DET iajs-1988 103 267 processes process NOUN iajs-1988 103 268 choose choose VERB iajs-1988 103 269 ℒ∗ ℒ∗ ADJ iajs-1988 103 270 satisfy satisfy NOUN iajs-1988 103 271 : : PUNCT iajs-1988 104 1 𝒢 𝒢 ADP iajs-1988 104 2 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 104 3 𝑟 𝑟 X iajs-1988 104 4 , , PUNCT iajs-1988 104 5 𝒯 𝒯 PROPN iajs-1988 104 6 𝒯 𝒯 PROPN iajs-1988 104 7 … … PUNCT iajs-1988 104 8 𝒯 𝒯 PROPN iajs-1988 104 9 𝑟 𝑟 NOUN iajs-1988 104 10 , , PUNCT iajs-1988 104 11 𝑟 𝑟 X iajs-1988 104 12 , , PUNCT iajs-1988 104 13 … … PUNCT iajs-1988 104 14 … … PUNCT iajs-1988 104 15 , , PUNCT iajs-1988 104 16 𝑟 𝑟 X iajs-1988 104 17 , , PUNCT iajs-1988 104 18 ℒ∗ ℒ∗ ADV iajs-1988 104 19 𝒢 𝒢 PROPN iajs-1988 104 20 𝒯 𝒯 PROPN iajs-1988 104 21 𝒯 𝒯 PROPN iajs-1988 104 22 … … PUNCT iajs-1988 104 23 𝒯 𝒯 PROPN iajs-1988 104 24 𝑟 𝑟 NOUN iajs-1988 104 25 , , PUNCT iajs-1988 104 26 𝑟 𝑟 X iajs-1988 104 27 , , PUNCT iajs-1988 104 28 … … PUNCT iajs-1988 104 29 … … PUNCT iajs-1988 104 30 , , PUNCT iajs-1988 104 31 𝑟 𝑟 X iajs-1988 104 32 , , PUNCT iajs-1988 104 33 ℒ∗ ℒ∗ ADV iajs-1988 104 34 , , PUNCT iajs-1988 104 35 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 104 36 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 104 37 𝑥 𝑥 PROPN iajs-1988 105 1 𝒢 𝒢 PROPN iajs-1988 105 2 𝒯 𝒯 PROPN iajs-1988 105 3 𝒯 𝒯 PROPN iajs-1988 105 4 … … PUNCT iajs-1988 105 5 𝒯 𝒯 PROPN iajs-1988 105 6 𝑟 𝑟 NOUN iajs-1988 105 7 , , PUNCT iajs-1988 105 8 𝑟 𝑟 X iajs-1988 105 9 , , PUNCT iajs-1988 105 10 … … PUNCT iajs-1988 105 11 … … PUNCT iajs-1988 105 12 , , PUNCT iajs-1988 105 13 𝑟 𝑟 NOUN iajs-1988 105 14 , , PUNCT iajs-1988 105 15 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 16 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 17 𝑥 𝑥 PROPN iajs-1988 105 18 , , PUNCT iajs-1988 105 19 ℒ∗ ℒ∗ ADV iajs-1988 105 20 𝒢 𝒢 PROPN iajs-1988 105 21 𝒯 𝒯 PROPN iajs-1988 105 22 𝒯 𝒯 PROPN iajs-1988 105 23 … … PUNCT iajs-1988 105 24 𝒯 𝒯 PROPN iajs-1988 105 25 𝑟 𝑟 NOUN iajs-1988 105 26 , , PUNCT iajs-1988 105 27 𝑟 𝑟 X iajs-1988 105 28 , , PUNCT iajs-1988 105 29 … … PUNCT iajs-1988 105 30 … … PUNCT iajs-1988 105 31 , , PUNCT iajs-1988 105 32 𝑟 𝑟 X iajs-1988 105 33 , , PUNCT iajs-1988 105 34 𝒯 𝒯 PROPN iajs-1988 105 35 𝒯 𝒯 PROPN iajs-1988 105 36 … … PUNCT iajs-1988 105 37 𝒯 𝒯 PROPN iajs-1988 105 38 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 39 𝑥 𝑥 PROPN iajs-1988 105 40 , , PUNCT iajs-1988 105 41 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 42 𝑥 𝑥 X iajs-1988 105 43 , , PUNCT iajs-1988 105 44 … … PUNCT iajs-1988 105 45 … … PUNCT iajs-1988 105 46 , , PUNCT iajs-1988 105 47 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 48 𝑥 𝑥 X iajs-1988 105 49 , , PUNCT iajs-1988 105 50 ℒ∗ ℒ∗ ADV iajs-1988 105 51 𝓌 𝓌 DET iajs-1988 105 52 max max PROPN iajs-1988 105 53 𝜔 𝜔 PROPN iajs-1988 105 54 𝒢 𝒢 PROPN iajs-1988 105 55 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 56 𝑟 𝑟 NOUN iajs-1988 105 57 , , PUNCT iajs-1988 105 58 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 59 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 60 𝑥 𝑥 PROPN iajs-1988 105 61 , , PUNCT iajs-1988 105 62 ℒ∗ ℒ∗ ADV iajs-1988 105 63 , , PUNCT iajs-1988 105 64 𝜔 𝜔 PROPN iajs-1988 105 65 𝒢 𝒢 PROPN iajs-1988 105 66 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 67 𝑟 𝑟 NOUN iajs-1988 105 68 , , PUNCT iajs-1988 105 69 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 70 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 71 𝑥 𝑥 PROPN iajs-1988 105 72 , , PUNCT iajs-1988 105 73 ℒ∗ ℒ∗ ADV iajs-1988 105 74 , , PUNCT iajs-1988 105 75 … … PUNCT iajs-1988 105 76 … … PUNCT iajs-1988 105 77 , , PUNCT iajs-1988 105 78 𝜔 𝜔 X iajs-1988 105 79 𝒢 𝒢 PROPN iajs-1988 105 80 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 81 𝑟 𝑟 NOUN iajs-1988 105 82 , , PUNCT iajs-1988 105 83 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 84 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 85 𝑥 𝑥 PROPN iajs-1988 105 86 , , PUNCT iajs-1988 105 87 ℒ∗ ℒ∗ ADV iajs-1988 105 88 𝓌 𝓌 PRON iajs-1988 105 89 max max PROPN iajs-1988 105 90 𝒢 𝒢 PROPN iajs-1988 105 91 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 92 𝑟 𝑟 NOUN iajs-1988 105 93 , , PUNCT iajs-1988 105 94 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 95 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 96 𝑥 𝑥 PROPN iajs-1988 105 97 , , PUNCT iajs-1988 105 98 ℒ∗ ℒ∗ ADV iajs-1988 105 99 , , PUNCT iajs-1988 105 100 𝒢 𝒢 PROPN iajs-1988 105 101 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 102 𝑟 𝑟 NOUN iajs-1988 105 103 , , PUNCT iajs-1988 105 104 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 105 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 106 𝑥 𝑥 PROPN iajs-1988 105 107 , , PUNCT iajs-1988 105 108 ℒ∗ ℒ∗ ADV iajs-1988 105 109 , , PUNCT iajs-1988 105 110 … … PUNCT iajs-1988 105 111 … … PUNCT iajs-1988 105 112 , , PUNCT iajs-1988 105 113 𝒢 𝒢 PROPN iajs-1988 105 114 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 115 𝑟 𝑟 NOUN iajs-1988 105 116 , , PUNCT iajs-1988 105 117 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 118 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 119 𝑥 𝑥 PROPN iajs-1988 105 120 , , PUNCT iajs-1988 105 121 ℒ∗ ℒ∗ ADJ iajs-1988 105 122 but but CCONJ iajs-1988 105 123 , , PUNCT iajs-1988 105 124 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 125 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 126 𝑥 𝑥 PROPN iajs-1988 105 127 is be AUX iajs-1988 105 128 𝒢–convergent 𝒢–convergent ADJ iajs-1988 105 129 to to ADP iajs-1988 105 130 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 105 131 𝑟 𝑟 NOUN iajs-1988 105 132             SPACE iajs-1988 105 133 164 164 NUM iajs-1988 105 134     SPACE iajs-1988 105 135 ibn ibn PROPN iajs-1988 105 136 al al PROPN iajs-1988 105 137 - - PUNCT iajs-1988 105 138 haitham haitham PROPN iajs-1988 105 139 jour jour X iajs-1988 105 140 . . PROPN iajs-1988 106 1 for for ADP iajs-1988 106 2 pure pure ADJ iajs-1988 106 3 & & CCONJ iajs-1988 106 4 appl.sci appl.sci PROPN iajs-1988 106 5 . . PUNCT iajs-1988 107 1 ihjpas ihjpas PROPN iajs-1988 107 2 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 107 3 vol vol NOUN iajs-1988 107 4 . . PUNCT iajs-1988 108 1 32 32 NUM iajs-1988 108 2 ( ( PUNCT iajs-1988 108 3 1 1 NUM iajs-1988 108 4 ) ) PUNCT iajs-1988 108 5 2019 2019 NUM iajs-1988 108 6 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 7 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 8 𝑥 𝑥 PROPN iajs-1988 108 9 is be AUX iajs-1988 108 10 𝒢–convergent 𝒢–convergent ADJ iajs-1988 108 11 to to ADP iajs-1988 108 12 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 13 𝑟 𝑟 NOUN iajs-1988 108 14 ⋮ ⋮ NOUN iajs-1988 108 15 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 16 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 17 𝑥 𝑥 PROPN iajs-1988 108 18 is be AUX iajs-1988 108 19 𝒢–convergent 𝒢–convergent ADJ iajs-1988 108 20 to to ADP iajs-1988 108 21 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 22 𝑟 𝑟 PRON iajs-1988 108 23 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 24 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 25 𝑥 𝑥 PROPN iajs-1988 108 26 is be AUX iajs-1988 108 27 𝒢–convergent 𝒢–convergent ADJ iajs-1988 108 28 to to ADP iajs-1988 108 29 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 30 𝑟 𝑟 NOUN iajs-1988 108 31 which which PRON iajs-1988 108 32 is be AUX iajs-1988 108 33 implies implie NOUN iajs-1988 108 34 , , PUNCT iajs-1988 108 35 by by ADP iajs-1988 108 36 definition definition NOUN iajs-1988 108 37 of of ADP iajs-1988 108 38 𝒢–convergent 𝒢–convergent NOUN iajs-1988 108 39 in in ADP iajs-1988 108 40 𝐺–metric 𝐺–metric ADJ iajs-1988 108 41 space space NOUN iajs-1988 108 42 , , PUNCT iajs-1988 108 43 𝒢 𝒢 PROPN iajs-1988 108 44 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 108 45 𝑟 𝑟 NOUN iajs-1988 108 46 , , PUNCT iajs-1988 108 47 𝑓 𝑓 DET iajs-1988 108 48 𝑟 𝑟 NOUN iajs-1988 108 49 , , PUNCT iajs-1988 108 50 𝑟 𝑟 X iajs-1988 108 51 , , PUNCT iajs-1988 108 52 … … PUNCT iajs-1988 108 53 … … PUNCT iajs-1988 108 54 , , PUNCT iajs-1988 108 55 𝑟 𝑟 X iajs-1988 108 56 , , PUNCT iajs-1988 108 57 ℒ∗ ℒ∗ ADV iajs-1988 108 58 0 0 NUM iajs-1988 108 59 ⇒ ⇒ NOUN iajs-1988 108 60 𝒯 𝒯 PROPN iajs-1988 108 61 𝒯 𝒯 PROPN iajs-1988 108 62 … … PUNCT iajs-1988 108 63 𝒯 𝒯 PROPN iajs-1988 108 64 𝑟 𝑟 NOUN iajs-1988 108 65 , , PUNCT iajs-1988 108 66 𝑟 𝑟 X iajs-1988 108 67 , , PUNCT iajs-1988 108 68 … … PUNCT iajs-1988 108 69 … … PUNCT iajs-1988 108 70 , , PUNCT iajs-1988 108 71 𝑟 𝑟 X iajs-1988 108 72 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 108 73 𝑟 𝑟 NOUN iajs-1988 109 1 so so SCONJ iajs-1988 109 2 𝑟 𝑟 NOUN iajs-1988 109 3 , , PUNCT iajs-1988 109 4 𝑟 𝑟 X iajs-1988 109 5 , , PUNCT iajs-1988 109 6 … … PUNCT iajs-1988 109 7 … … PUNCT iajs-1988 109 8 , , PUNCT iajs-1988 109 9 𝑟 𝑟 PRON iajs-1988 109 10 is be AUX iajs-1988 109 11 a a DET iajs-1988 109 12 modified modify VERB iajs-1988 109 13 tupled tuple VERB iajs-1988 109 14 coincidence coincidence NOUN iajs-1988 109 15 point point NOUN iajs-1988 109 16 of of ADP iajs-1988 109 17 𝒯 𝒯 PROPN iajs-1988 109 18 , , PUNCT iajs-1988 109 19 𝒯 𝒯 PROPN iajs-1988 109 20 , , PUNCT iajs-1988 109 21 … … PUNCT iajs-1988 109 22 , , PUNCT iajs-1988 109 23 𝒯 𝒯 PROPN iajs-1988 109 24 , , PUNCT iajs-1988 109 25 𝒰 𝒰 PROPN iajs-1988 109 26 𝑎𝑛𝑑 𝑎𝑛𝑑 ADJ iajs-1988 109 27 𝒱. 𝒱. PROPN iajs-1988 109 28 from from ADP iajs-1988 109 29 theorem(8),we theorem(8),we NOUN iajs-1988 109 30 can can AUX iajs-1988 109 31 get get VERB iajs-1988 109 32 the the DET iajs-1988 109 33 following follow VERB iajs-1988 109 34 corollaries corollary NOUN iajs-1988 109 35 corollary corollary NOUN iajs-1988 109 36 9 9 NUM iajs-1988 109 37 let let VERB iajs-1988 109 38 𝑋 𝑋 PROPN iajs-1988 109 39 , , PUNCT iajs-1988 109 40 𝒢 𝒢 PROPN iajs-1988 109 41 , , PUNCT iajs-1988 109 42 be be AUX iajs-1988 109 43 a a DET iajs-1988 109 44 partiallyiordered partiallyiordere VERB iajs-1988 109 45 generalizedimetric generalizedimetric ADJ iajs-1988 109 46 space space NOUN iajs-1988 109 47 .under .under ADP iajs-1988 109 48 the the DET iajs-1988 109 49 same same ADJ iajs-1988 109 50 assumptionsiof assumptionsiof NOUN iajs-1988 109 51 theorem(8 theorem(8 PROPN iajs-1988 109 52 ) ) PUNCT iajs-1988 110 1 but but CCONJ iajs-1988 110 2 𝒢 𝒢 PROPN iajs-1988 110 3 𝒯 𝒯 PROPN iajs-1988 110 4 𝒯 𝒯 PROPN iajs-1988 110 5 ∗ ∗ NOUN iajs-1988 110 6 … … PUNCT iajs-1988 110 7 ∗ ∗ NOUN iajs-1988 110 8 𝒯 𝒯 PROPN iajs-1988 110 9 𝑥 𝑥 PROPN iajs-1988 110 10 , , PUNCT iajs-1988 110 11 𝑥 𝑥 X iajs-1988 110 12 , , PUNCT iajs-1988 110 13 … … PUNCT iajs-1988 110 14 , , PUNCT iajs-1988 110 15 𝑥 𝑥 INTJ iajs-1988 110 16 , , PUNCT iajs-1988 110 17 𝒯 𝒯 PROPN iajs-1988 110 18 𝒯 𝒯 PROPN iajs-1988 110 19 … … PUNCT iajs-1988 110 20 𝒯 𝒯 PROPN iajs-1988 110 21 𝑦 𝑦 PROPN iajs-1988 110 22 , , PUNCT iajs-1988 110 23 𝑦 𝑦 PRON iajs-1988 110 24 , , PUNCT iajs-1988 110 25 … … PUNCT iajs-1988 110 26 𝑦 𝑦 NOUN iajs-1988 110 27 , , PUNCT iajs-1988 110 28 ℒ ℒ NOUN iajs-1988 110 29 𝓌 𝓌 PROPN iajs-1988 110 30 1 1 NUM iajs-1988 110 31 𝑛 𝑛 PRON iajs-1988 110 32 𝜔 𝜔 NOUN iajs-1988 110 33 𝒢 𝒢 PROPN iajs-1988 110 34 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 35 𝑥 𝑥 NOUN iajs-1988 110 36 , , PUNCT iajs-1988 110 37 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 38 𝑦 𝑦 NOUN iajs-1988 110 39 , , PUNCT iajs-1988 110 40 ℒ ℒ PROPN iajs-1988 110 41 𝜔 𝜔 PROPN iajs-1988 110 42 𝒢 𝒢 PROPN iajs-1988 110 43 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 44 𝑥 𝑥 NOUN iajs-1988 110 45 , , PUNCT iajs-1988 110 46 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 47 𝑦 𝑦 NOUN iajs-1988 110 48 , , PUNCT iajs-1988 110 49 ℒ ℒ NOUN iajs-1988 110 50 ⋯ ⋯ ADP iajs-1988 110 51 𝜔 𝜔 NOUN iajs-1988 110 52 𝒢 𝒢 PROPN iajs-1988 110 53 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 54 𝑥 𝑥 NOUN iajs-1988 110 55 , , PUNCT iajs-1988 110 56 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 110 57 𝑦 𝑦 NOUN iajs-1988 110 58 , , PUNCT iajs-1988 110 59 ℒ ℒ PROPN iajs-1988 110 60 then then ADV iajs-1988 110 61 𝒯 𝒯 PROPN iajs-1988 110 62 , , PUNCT iajs-1988 110 63 𝒯 𝒯 PROPN iajs-1988 110 64 , , PUNCT iajs-1988 110 65 … … PUNCT iajs-1988 110 66 , , PUNCT iajs-1988 110 67 𝒯 𝒯 PROPN iajs-1988 110 68 , , PUNCT iajs-1988 110 69 𝒰 𝒰 PROPN iajs-1988 110 70 𝑎𝑛𝑑𝒱 𝑎𝑛𝑑𝒱 AUX iajs-1988 110 71 have have VERB iajs-1988 110 72 a a DET iajs-1988 110 73 modified modify VERB iajs-1988 110 74 tupled tuple VERB iajs-1988 110 75 coincidence coincidence NOUN iajs-1988 110 76 point point NOUN iajs-1988 110 77 . . PUNCT iajs-1988 111 1 corollary corollary ADJ iajs-1988 111 2 10 10 NUM iajs-1988 111 3 let let VERB iajs-1988 111 4 𝑋 𝑋 PROPN iajs-1988 111 5 , , PUNCT iajs-1988 111 6 𝐺 𝐺 PROPN iajs-1988 111 7 , , PUNCT iajs-1988 111 8 be be AUX iajs-1988 111 9 a a DET iajs-1988 111 10 partiallyiordered partiallyiordere VERB iajs-1988 111 11 generalized generalized ADJ iajs-1988 111 12 metric metric ADJ iajs-1988 111 13 space space NOUN iajs-1988 111 14 𝒢 𝒢 PROPN iajs-1988 111 15 𝒯 𝒯 PROPN iajs-1988 111 16 𝒯 𝒯 PROPN iajs-1988 111 17 ∗ ∗ NOUN iajs-1988 111 18 … … PUNCT iajs-1988 111 19 ∗ ∗ NOUN iajs-1988 111 20 𝒯 𝒯 PROPN iajs-1988 111 21 𝑥 𝑥 PROPN iajs-1988 111 22 , , PUNCT iajs-1988 111 23 𝑥 𝑥 X iajs-1988 111 24 , , PUNCT iajs-1988 111 25 … … PUNCT iajs-1988 111 26 , , PUNCT iajs-1988 111 27 𝑥 𝑥 INTJ iajs-1988 111 28 , , PUNCT iajs-1988 111 29 𝒯 𝒯 PROPN iajs-1988 111 30 𝒯 𝒯 PROPN iajs-1988 111 31 … … PUNCT iajs-1988 111 32 𝒯 𝒯 PROPN iajs-1988 111 33 𝑦 𝑦 PROPN iajs-1988 111 34 , , PUNCT iajs-1988 111 35 𝑦 𝑦 PRON iajs-1988 111 36 , , PUNCT iajs-1988 111 37 … … PUNCT iajs-1988 111 38 𝑦 𝑦 NOUN iajs-1988 111 39 , , PUNCT iajs-1988 111 40 ℒ ℒ NOUN iajs-1988 111 41 𝓌 𝓌 X iajs-1988 111 42 𝑘 𝑘 ADP iajs-1988 111 43 𝒢 𝒢 PROPN iajs-1988 111 44 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 45 𝑥 𝑥 NOUN iajs-1988 111 46 , , PUNCT iajs-1988 111 47 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 48 𝑦 𝑦 NOUN iajs-1988 111 49 , , PUNCT iajs-1988 111 50 ℒ ℒ PROPN iajs-1988 111 51 𝑘 𝑘 PROPN iajs-1988 111 52 𝒢 𝒢 PROPN iajs-1988 111 53 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 54 𝑥 𝑥 NOUN iajs-1988 111 55 , , PUNCT iajs-1988 111 56 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 57 𝑦 𝑦 NOUN iajs-1988 111 58 , , PUNCT iajs-1988 111 59 ℒ ℒ PROPN iajs-1988 111 60 ⋯ ⋯ ADP iajs-1988 111 61 𝑘 𝑘 PROPN iajs-1988 111 62 𝒢 𝒢 PROPN iajs-1988 111 63 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 64 𝑥 𝑥 NOUN iajs-1988 111 65 , , PUNCT iajs-1988 111 66 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 111 67 𝑦 𝑦 NOUN iajs-1988 111 68 , , PUNCT iajs-1988 111 69 ℒ ℒ NOUN iajs-1988 111 70 , , PUNCT iajs-1988 111 71 such such ADJ iajs-1988 111 72 that that SCONJ iajs-1988 111 73 𝑘 𝑘 PROPN iajs-1988 111 74 ∈ ∈ PROPN iajs-1988 111 75 0,1 0,1 NUM iajs-1988 111 76 𝑓𝑜𝑟 𝑓𝑜𝑟 NOUN iajs-1988 111 77 𝑎𝑙𝑙 𝑎𝑙𝑙 X iajs-1988 111 78 𝑖 𝑖 X iajs-1988 111 79 1,2 1,2 NUM iajs-1988 111 80 , , PUNCT iajs-1988 111 81 … … PUNCT iajs-1988 111 82 … … PUNCT iajs-1988 111 83 , , PUNCT iajs-1988 111 84 𝑛.then 𝑛.then NOUN iajs-1988 111 85 𝒯 𝒯 PROPN iajs-1988 111 86 , , PUNCT iajs-1988 111 87 𝒯 𝒯 PROPN iajs-1988 111 88 , , PUNCT iajs-1988 111 89 … … PUNCT iajs-1988 111 90 , , PUNCT iajs-1988 111 91 𝒯 𝒯 PROPN iajs-1988 111 92 , , PUNCT iajs-1988 111 93 𝒰 𝒰 PROPN iajs-1988 111 94 𝑎𝑛𝑑𝒱 𝑎𝑛𝑑𝒱 NOUN iajs-1988 111 95 have have VERB iajs-1988 111 96 a a DET iajs-1988 111 97 modifieditupled modifieditupled ADJ iajs-1988 111 98 coincidence coincidence NOUN iajs-1988 111 99 point point NOUN iajs-1988 111 100 . . PUNCT iajs-1988 112 1 corollary corollary ADJ iajs-1988 112 2 11 11 NUM iajs-1988 112 3 let let VERB iajs-1988 112 4 𝑋 𝑋 PROPN iajs-1988 112 5 , , PUNCT iajs-1988 112 6 𝒢 𝒢 PROPN iajs-1988 112 7 , , PUNCT iajs-1988 112 8 be be AUX iajs-1988 112 9 a a DET iajs-1988 112 10 partiallyiordered partiallyiordere VERB iajs-1988 112 11 generalizedimetric generalizedimetric ADJ iajs-1988 112 12 space space NOUN iajs-1988 112 13 .under .under ADP iajs-1988 112 14 the the DET iajs-1988 112 15 same same ADJ iajs-1988 112 16 assumptions assumption NOUN iajs-1988 112 17 of of ADP iajs-1988 112 18 theorem(8 theorem(8 PROPN iajs-1988 112 19 ) ) PUNCT iajs-1988 113 1 but but CCONJ iajs-1988 113 2 𝒢 𝒢 PROPN iajs-1988 113 3 𝒯 𝒯 PROPN iajs-1988 113 4 𝒯 𝒯 PROPN iajs-1988 113 5 ∗ ∗ NOUN iajs-1988 113 6 … … PUNCT iajs-1988 113 7 ∗ ∗ NOUN iajs-1988 113 8 𝒯 𝒯 PROPN iajs-1988 113 9 𝑥 𝑥 PROPN iajs-1988 113 10 , , PUNCT iajs-1988 113 11 𝑥 𝑥 X iajs-1988 113 12 , , PUNCT iajs-1988 113 13 … … PUNCT iajs-1988 113 14 , , PUNCT iajs-1988 113 15 𝑥 𝑥 INTJ iajs-1988 113 16 , , PUNCT iajs-1988 113 17 𝒯 𝒯 PROPN iajs-1988 113 18 𝒯 𝒯 PROPN iajs-1988 113 19 … … PUNCT iajs-1988 113 20 𝒯 𝒯 PROPN iajs-1988 113 21 𝑦 𝑦 PROPN iajs-1988 113 22 , , PUNCT iajs-1988 113 23 𝑦 𝑦 PRON iajs-1988 113 24 , , PUNCT iajs-1988 113 25 … … PUNCT iajs-1988 113 26 𝑦 𝑦 NOUN iajs-1988 113 27 , , PUNCT iajs-1988 113 28 ℒ ℒ PROPN iajs-1988 113 29 𝓌 𝓌 X iajs-1988 113 30 max max PROPN iajs-1988 113 31 𝑘 𝑘 PROPN iajs-1988 113 32 𝒢 𝒢 PROPN iajs-1988 113 33 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 34 𝑥 𝑥 NOUN iajs-1988 113 35 , , PUNCT iajs-1988 113 36 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 37 𝑦 𝑦 NOUN iajs-1988 113 38 , , PUNCT iajs-1988 113 39 ℒ ℒ PROPN iajs-1988 113 40 , , PUNCT iajs-1988 113 41 𝑘 𝑘 DET iajs-1988 113 42 𝒢 𝒢 PROPN iajs-1988 113 43 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 44 𝑥 𝑥 NOUN iajs-1988 113 45 , , PUNCT iajs-1988 113 46 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 47 𝑦 𝑦 NOUN iajs-1988 113 48 , , PUNCT iajs-1988 113 49 ℒ ℒ NOUN iajs-1988 113 50 , , PUNCT iajs-1988 113 51 … … PUNCT iajs-1988 113 52 , , PUNCT iajs-1988 113 53 𝑘 𝑘 X iajs-1988 113 54 𝒢 𝒢 PROPN iajs-1988 113 55 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 56 𝑥 𝑥 NOUN iajs-1988 113 57 , , PUNCT iajs-1988 113 58 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 113 59 𝑦 𝑦 NOUN iajs-1988 113 60 , , PUNCT iajs-1988 113 61 ℒ ℒ X iajs-1988 113 62             SPACE iajs-1988 113 63 165 165 NUM iajs-1988 113 64     SPACE iajs-1988 113 65 ibn ibn PROPN iajs-1988 113 66 al al PROPN iajs-1988 113 67 - - PUNCT iajs-1988 113 68 haitham haitham PROPN iajs-1988 113 69 jour jour X iajs-1988 113 70 . . PROPN iajs-1988 113 71 for for ADP iajs-1988 113 72 pure pure ADJ iajs-1988 113 73 & & CCONJ iajs-1988 113 74 appl.sci appl.sci PROPN iajs-1988 113 75 . . PUNCT iajs-1988 113 76 ihjpas ihjpas PROPN iajs-1988 113 77 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 113 78 vol vol NOUN iajs-1988 113 79 . . PUNCT iajs-1988 114 1 32 32 NUM iajs-1988 114 2 ( ( PUNCT iajs-1988 114 3 1 1 NUM iajs-1988 114 4 ) ) PUNCT iajs-1988 114 5 2019 2019 NUM iajs-1988 114 6 such such ADJ iajs-1988 114 7 that that SCONJ iajs-1988 114 8 𝑘 𝑘 PROPN iajs-1988 114 9 ∈ ∈ PROPN iajs-1988 114 10 0,1 0,1 NUM iajs-1988 114 11 𝑓𝑜𝑟 𝑓𝑜𝑟 NOUN iajs-1988 114 12 𝑎𝑙𝑙 𝑎𝑙𝑙 X iajs-1988 114 13 𝑖 𝑖 X iajs-1988 114 14 1,2 1,2 NUM iajs-1988 114 15 , , PUNCT iajs-1988 114 16 … … PUNCT iajs-1988 114 17 … … PUNCT iajs-1988 114 18 , , PUNCT iajs-1988 114 19 𝑛.then 𝑛.then NOUN iajs-1988 114 20 𝒯 𝒯 PROPN iajs-1988 114 21 , , PUNCT iajs-1988 114 22 𝒯 𝒯 PROPN iajs-1988 114 23 , , PUNCT iajs-1988 114 24 … … PUNCT iajs-1988 114 25 , , PUNCT iajs-1988 114 26 𝒯 𝒯 PROPN iajs-1988 114 27 , , PUNCT iajs-1988 114 28 𝒰 𝒰 PROPN iajs-1988 114 29 𝑎𝑛𝑑𝒱 𝑎𝑛𝑑𝒱 NOUN iajs-1988 114 30 have have VERB iajs-1988 114 31 a a DET iajs-1988 114 32 modified modify VERB iajs-1988 114 33 tupled tuple VERB iajs-1988 114 34 tupled tuple VERB iajs-1988 114 35 coincidenceipoint coincidenceipoint NOUN iajs-1988 114 36 . . PUNCT iajs-1988 115 1 corollary corollary ADJ iajs-1988 115 2 12 12 NUM iajs-1988 115 3 let let VERB iajs-1988 115 4 𝑋 𝑋 PROPN iajs-1988 115 5 , , PUNCT iajs-1988 115 6 𝒢 𝒢 PROPN iajs-1988 115 7 , , PUNCT iajs-1988 115 8 be be AUX iajs-1988 115 9 a a DET iajs-1988 115 10 partiallyiordered partiallyiordere VERB iajs-1988 115 11 generalizedimetric generalizedimetric ADJ iajs-1988 115 12 space space NOUN iajs-1988 115 13 .under .under ADP iajs-1988 115 14 the the DET iajs-1988 115 15 same same ADJ iajs-1988 115 16 assumptions assumption NOUN iajs-1988 115 17 of of ADP iajs-1988 115 18 theorem(8 theorem(8 PROPN iajs-1988 115 19 ) ) PUNCT iajs-1988 116 1 but but CCONJ iajs-1988 116 2 𝒢 𝒢 PROPN iajs-1988 116 3 𝒯 𝒯 PROPN iajs-1988 116 4 𝒯 𝒯 PROPN iajs-1988 116 5 ∗ ∗ NOUN iajs-1988 116 6 … … PUNCT iajs-1988 116 7 ∗ ∗ NOUN iajs-1988 116 8 𝒯 𝒯 PROPN iajs-1988 116 9 𝑥 𝑥 PROPN iajs-1988 116 10 , , PUNCT iajs-1988 116 11 𝑥 𝑥 X iajs-1988 116 12 , , PUNCT iajs-1988 116 13 … … PUNCT iajs-1988 116 14 , , PUNCT iajs-1988 116 15 𝑥 𝑥 INTJ iajs-1988 116 16 , , PUNCT iajs-1988 116 17 𝒯 𝒯 PROPN iajs-1988 116 18 𝒯 𝒯 PROPN iajs-1988 116 19 … … PUNCT iajs-1988 116 20 𝒯 𝒯 PROPN iajs-1988 116 21 𝑦 𝑦 PROPN iajs-1988 116 22 , , PUNCT iajs-1988 116 23 𝑦 𝑦 PRON iajs-1988 116 24 , , PUNCT iajs-1988 116 25 … … PUNCT iajs-1988 116 26 𝑦 𝑦 NOUN iajs-1988 116 27 , , PUNCT iajs-1988 116 28 ℒ ℒ PROPN iajs-1988 116 29 𝒢 𝒢 PROPN iajs-1988 116 30 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 116 31 , , PUNCT iajs-1988 116 32 𝒰𝒱 𝒰𝒱 NOUN iajs-1988 116 33 ℒ ℒ NOUN iajs-1988 116 34 𝒢 𝒢 PROPN iajs-1988 116 35 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 116 36 , , PUNCT iajs-1988 116 37 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 116 38 , , PUNCT iajs-1988 116 39 ℒ ℒ PROPN iajs-1988 116 40 ⋯ ⋯ PROPN iajs-1988 116 41 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 116 42 , , PUNCT iajs-1988 116 43 𝒰𝒱 𝒰𝒱 PROPN iajs-1988 116 44 , , PUNCT iajs-1988 116 45 ℒ ℒ NOUN iajs-1988 116 46 . . PUNCT iajs-1988 117 1 then then ADV iajs-1988 117 2 𝒯 𝒯 PROPN iajs-1988 117 3 , , PUNCT iajs-1988 117 4 𝒯 𝒯 PROPN iajs-1988 117 5 , , PUNCT iajs-1988 117 6 … … PUNCT iajs-1988 117 7 , , PUNCT iajs-1988 117 8 𝒯 𝒯 PROPN iajs-1988 117 9 , , PUNCT iajs-1988 117 10 𝒰 𝒰 PROPN iajs-1988 117 11 𝑎𝑛𝑑𝒱 𝑎𝑛𝑑𝒱 AUX iajs-1988 117 12 have have VERB iajs-1988 117 13 a a DET iajs-1988 117 14 modified modify VERB iajs-1988 117 15 tupled tuple VERB iajs-1988 117 16 coincidence coincidence NOUN iajs-1988 117 17 point point NOUN iajs-1988 117 18 . . PUNCT iajs-1988 118 1 4.conclusion 4.conclusion NUM iajs-1988 118 2 the the DET iajs-1988 118 3 new new ADJ iajs-1988 118 4 concepts concept NOUN iajs-1988 118 5 of of ADP iajs-1988 118 6 modified modify VERB iajs-1988 118 7 tupledicoincidence tupledicoincidence NOUN iajs-1988 118 8 points point NOUN iajs-1988 118 9 and and CCONJ iajs-1988 118 10 mixed mixed ADJ iajs-1988 118 11 finite finite NOUN iajs-1988 118 12 monotone monotone ADJ iajs-1988 118 13 property property NOUN iajs-1988 118 14 are be AUX iajs-1988 118 15 introduced introduce VERB iajs-1988 118 16 . . PUNCT iajs-1988 119 1 also also ADV iajs-1988 119 2 , , PUNCT iajs-1988 119 3 we we PRON iajs-1988 119 4 established establish VERB iajs-1988 119 5 some some DET iajs-1988 119 6 modified modify VERB iajs-1988 119 7 tupled tuple VERB iajs-1988 119 8 coincidence coincidence NOUN iajs-1988 119 9 theorems theorem NOUN iajs-1988 119 10 in in ADP iajs-1988 119 11 partially partially ADV iajs-1988 119 12 ordered order VERB iajs-1988 119 13 generalized generalized ADJ iajs-1988 119 14 metric metric ADJ iajs-1988 119 15 space space NOUN iajs-1988 119 16 . . PUNCT iajs-1988 119 17     SPACE iajs-1988 119 18 references reference NOUN iajs-1988 119 19 1 1 NUM iajs-1988 119 20 . . PUNCT iajs-1988 120 1 dhage dhage NOUN iajs-1988 120 2 , , PUNCT iajs-1988 120 3 b.generalized b.generalized ADJ iajs-1988 120 4 metric metric ADJ iajs-1988 120 5 space space NOUN iajs-1988 120 6 and and CCONJ iajs-1988 120 7 topological topological ADJ iajs-1988 120 8 structure structure NOUN iajs-1988 120 9 . . PUNCT iajs-1988 121 1 i. i. PROPN iajs-1988 121 2 analele analele VERB iajs-1988 121 3 scientific scientific ADJ iajs-1988 121 4 ale ale NOUN iajs-1988 121 5 universities university NOUN iajs-1988 121 6 ai.i ai.i NOUN iajs-1988 121 7 . . PUNCT iajs-1988 121 8 ” " PUNCT iajs-1988 122 1 cuzadin cuzadin VERB iajs-1988 122 2 lasi lasi PROPN iajs-1988 122 3 , , PUNCT iajs-1988 122 4 sieve sieve NOUN iajs-1988 122 5 nona nona PROPN iajs-1988 122 6 . . PUNCT iajs-1988 123 1 matematca matematca PROPN iajs-1988 123 2 . . PUNCT iajs-1988 124 1 2000 2000 NUM iajs-1988 124 2 , , PUNCT iajs-1988 124 3 47 47 NUM iajs-1988 124 4 , , PUNCT iajs-1988 124 5 3 3 NUM iajs-1988 124 6 - - SYM iajs-1988 124 7 24 24 NUM iajs-1988 124 8 . . PUNCT iajs-1988 125 1 2 2 NUM iajs-1988 125 2 . . X iajs-1988 125 3 mustafa mustafa PROPN iajs-1988 125 4 , , PUNCT iajs-1988 125 5 z. z. PROPN iajs-1988 125 6 ; ; PUNCT iajs-1988 125 7 partiallyiordered partiallyiordere VERB iajs-1988 125 8 generalizedimetric generalizedimetric ADJ iajs-1988 125 9 space space NOUN iajs-1988 125 10 sims sim NOUN iajs-1988 125 11 . . PUNCT iajs-1988 126 1 a a DET iajs-1988 126 2 new new ADJ iajs-1988 126 3 approach approach NOUN iajs-1988 126 4 to to ADP iajs-1988 126 5 generalized generalize VERB iajs-1988 126 6 metric metric ADJ iajs-1988 126 7 space space NOUN iajs-1988 126 8 . . PUNCT iajs-1988 127 1 journal journal PROPN iajs-1988 127 2 of of ADP iajs-1988 127 3 nonlinear nonlinear ADJ iajs-1988 127 4 and and CCONJ iajs-1988 127 5 convex convex ADJ iajs-1988 127 6 analysis analysis NOUN iajs-1988 127 7 . . PUNCT iajs-1988 128 1 2006,7 2006,7 NOUN iajs-1988 128 2 , , PUNCT iajs-1988 128 3 289 289 NUM iajs-1988 128 4 - - SYM iajs-1988 128 5 297 297 NUM iajs-1988 128 6 . . PUNCT iajs-1988 129 1 3 3 X iajs-1988 129 2 . . X iajs-1988 129 3 gnanbhaskar gnanbhaskar PROPN iajs-1988 129 4 , , PUNCT iajs-1988 129 5 t. t. PROPN iajs-1988 129 6 ; ; PUNCT iajs-1988 129 7 lakshmikantham lakshmikantham PROPN iajs-1988 129 8 , , PUNCT iajs-1988 129 9 v.fixed v.fixe VERB iajs-1988 129 10 point point NOUN iajs-1988 129 11 theorems theorem NOUN iajs-1988 129 12 in in ADP iajs-1988 129 13 partially partially ADV iajs-1988 129 14 ordered order VERB iajs-1988 129 15 metric metric ADJ iajs-1988 129 16 spaces space NOUN iajs-1988 129 17 and and CCONJ iajs-1988 129 18 applications application NOUN iajs-1988 129 19 . . PUNCT iajs-1988 130 1 nonlinear nonlinear ADJ iajs-1988 130 2 analysis analysis NOUN iajs-1988 130 3 . . PUNCT iajs-1988 131 1 2006 2006 NUM iajs-1988 131 2 , , PUNCT iajs-1988 131 3 65 65 NUM iajs-1988 131 4 , , PUNCT iajs-1988 131 5 79 79 NUM iajs-1988 131 6 - - SYM iajs-1988 131 7 93 93 NUM iajs-1988 131 8 . . PUNCT iajs-1988 132 1 4 4 NUM iajs-1988 132 2 . . X iajs-1988 132 3 lakshmikantham lakshmikantham ADJ iajs-1988 132 4 , , PUNCT iajs-1988 132 5 v. v. ADV iajs-1988 132 6 ; ; PUNCT iajs-1988 132 7 ciric ciric ADJ iajs-1988 132 8 , , PUNCT iajs-1988 132 9 l.coupled l.couple VERB iajs-1988 132 10 fixed fix VERB iajs-1988 132 11 point point NOUN iajs-1988 132 12 theorems theorem NOUN iajs-1988 132 13 for for ADP iajs-1988 132 14 nonlinear nonlinear ADJ iajs-1988 132 15 contractions contraction NOUN iajs-1988 132 16 in in ADP iajs-1988 132 17 partially partially ADV iajs-1988 132 18 ordered order VERB iajs-1988 132 19 metric metric ADJ iajs-1988 132 20 spaces space NOUN iajs-1988 132 21 . . PUNCT iajs-1988 133 1 nonlinear nonlinear ADJ iajs-1988 133 2 analysis analysis NOUN iajs-1988 133 3 . . PUNCT iajs-1988 134 1 2009,12 2009,12 NUM iajs-1988 134 2 , , PUNCT iajs-1988 134 3 43 43 NUM iajs-1988 134 4 - - SYM iajs-1988 134 5 49 49 NUM iajs-1988 134 6 . . PUNCT iajs-1988 135 1 5 5 NUM iajs-1988 135 2 . . X iajs-1988 135 3 berind berind NOUN iajs-1988 135 4 , , PUNCT iajs-1988 135 5 v. v. ADV iajs-1988 135 6 ; ; PUNCT iajs-1988 135 7 borcut borcut VERB iajs-1988 135 8 , , PUNCT iajs-1988 135 9 m. m. NOUN iajs-1988 135 10 tripled triple VERB iajs-1988 135 11 fixed fix VERB iajs-1988 135 12 point point NOUN iajs-1988 135 13 theorems theorem NOUN iajs-1988 135 14 for for ADP iajs-1988 135 15 contractive contractive ADJ iajs-1988 135 16 type type NOUN iajs-1988 135 17 mappings mapping NOUN iajs-1988 135 18 in in ADP iajs-1988 135 19 partially partially ADV iajs-1988 135 20 ordered order VERB iajs-1988 135 21 metric metric ADJ iajs-1988 135 22 spaces space NOUN iajs-1988 135 23 , , PUNCT iajs-1988 135 24 nonlinear nonlinear ADJ iajs-1988 135 25 theory theory NOUN iajs-1988 135 26 , , PUNCT iajs-1988 135 27 method method NOUN iajs-1988 135 28 & & CCONJ iajs-1988 135 29 applications application NOUN iajs-1988 135 30 . . PUNCT iajs-1988 136 1 2011,74 2011,74 NUM iajs-1988 136 2 , , PUNCT iajs-1988 136 3 89 89 NUM iajs-1988 136 4 - - SYM iajs-1988 136 5 97 97 NUM iajs-1988 136 6 . . NOUN iajs-1988 137 1 6 6 NUM iajs-1988 137 2 . . X iajs-1988 137 3 berind berind NOUN iajs-1988 137 4 , , PUNCT iajs-1988 137 5 v. v. ADV iajs-1988 137 6 ; ; PUNCT iajs-1988 137 7 borcut borcut VERB iajs-1988 137 8 , , PUNCT iajs-1988 137 9 m.tripled m.triple VERB iajs-1988 137 10 coincidence coincidence NOUN iajs-1988 137 11 theorems theorem NOUN iajs-1988 137 12 for for ADP iajs-1988 137 13 contractive contractive ADJ iajs-1988 137 14 type type NOUN iajs-1988 137 15 mappings mapping NOUN iajs-1988 137 16 in in ADP iajs-1988 137 17 partially partially ADV iajs-1988 137 18 ordered order VERB iajs-1988 137 19 metric.appl.mathematics metric.appl.mathematic NOUN iajs-1988 137 20 and and CCONJ iajs-1988 137 21 computer computer NOUN iajs-1988 137 22 . . PUNCT iajs-1988 138 1 2012,218 2012,218 NUM iajs-1988 138 2 , , PUNCT iajs-1988 138 3 29 29 NUM iajs-1988 138 4 - - SYM iajs-1988 138 5 36 36 NUM iajs-1988 138 6 . . PUNCT iajs-1988 138 7 7 7 X iajs-1988 138 8 . . X iajs-1988 138 9 savitri savitri PROPN iajs-1988 138 10 , , PUNCT iajs-1988 138 11 e. e. PROPN iajs-1988 138 12 ; ; PUNCT iajs-1988 138 13 hooda hooda PROPN iajs-1988 138 14 , , PUNCT iajs-1988 138 15 n. n. PROPN iajs-1988 138 16 fixed fix VERB iajs-1988 138 17 point point NOUN iajs-1988 138 18 theorems theorem NOUN iajs-1988 138 19 for for ADP iajs-1988 138 20 mapping mapping NOUN iajs-1988 138 21 having have VERB iajs-1988 138 22 the the DET iajs-1988 138 23 mixed mixed ADJ iajs-1988 138 24 monotone monotone ADJ iajs-1988 138 25 property property NOUN iajs-1988 138 26 . . PUNCT iajs-1988 139 1 tnt tnt PROPN iajs-1988 139 2 . . PUNCT iajs-1988 140 1 ach ach PROPN iajs-1988 140 2 . . PUNCT iajs-1988 141 1 app app PROPN iajs-1988 141 2 . . PUNCT iajs-1988 142 1 sci sci PROPN iajs-1988 142 2 . . PROPN iajs-1988 142 3 technol technol PROPN iajs-1988 142 4 . . PROPN iajs-1988 143 1 2011 2011 NUM iajs-1988 143 2 , , PUNCT iajs-1988 143 3 2 2 NUM iajs-1988 143 4 , , PUNCT iajs-1988 143 5 19 19 NUM iajs-1988 143 6 - - SYM iajs-1988 143 7 23 23 NUM iajs-1988 143 8 . . NOUN iajs-1988 144 1 8 8 NUM iajs-1988 144 2 . . X iajs-1988 144 3 shatanawi shatanawi PROPN iajs-1988 144 4 , , PUNCT iajs-1988 144 5 w. w. PROPN iajs-1988 144 6 ; ; PUNCT iajs-1988 144 7 postolache postolache NOUN iajs-1988 144 8 , , PUNCT iajs-1988 144 9 m. m. NOUN iajs-1988 144 10 ; ; PUNCT iajs-1988 144 11 mustafa mustafa PROPN iajs-1988 144 12 , , PUNCT iajs-1988 144 13 z. z. PROPN iajs-1988 144 14 tripled triple VERB iajs-1988 144 15 and and CCONJ iajs-1988 144 16 coincidence coincidence VERB iajs-1988 144 17 fixed fix VERB iajs-1988 144 18 point point NOUN iajs-1988 144 19 theorems theorem NOUN iajs-1988 144 20 for for ADP iajs-1988 144 21 contractive contractive ADJ iajs-1988 144 22 mappings mapping NOUN iajs-1988 144 23 satisfying satisfy VERB iajs-1988 144 24 ɸ ɸ NOUN iajs-1988 144 25 - - PUNCT iajs-1988 144 26 maps map NOUN iajs-1988 144 27 in in ADP iajs-1988 144 28 partially partially ADV iajs-1988 144 29 ordered order VERB iajs-1988 144 30 metric metric ADJ iajs-1988 144 31 spaces space NOUN iajs-1988 144 32 . . PUNCT iajs-1988 145 1 an an DET iajs-1988 145 2 . . PUNCT iajs-1988 145 3 st st PROPN iajs-1988 145 4 . . PROPN iajs-1988 145 5 univ univ PROPN iajs-1988 145 6 . . PUNCT iajs-1988 146 1 ovidius ovidius PROPN iajs-1988 146 2 constants constant NOUN iajs-1988 146 3 . . PUNCT iajs-1988 147 1 2014 2014 NUM iajs-1988 147 2 , , PUNCT iajs-1988 147 3 22 22 NUM iajs-1988 147 4 , , PUNCT iajs-1988 147 5 179 179 NUM iajs-1988 147 6 - - SYM iajs-1988 147 7 200 200 NUM iajs-1988 147 8 . . PUNCT iajs-1988 147 9             SPACE iajs-1988 148 1 166 166 NUM iajs-1988 148 2     SPACE iajs-1988 148 3 ibn ibn PROPN iajs-1988 148 4 al al PROPN iajs-1988 148 5 - - PUNCT iajs-1988 148 6 haitham haitham PROPN iajs-1988 148 7 jour jour X iajs-1988 148 8 . . PROPN iajs-1988 148 9 for for ADP iajs-1988 148 10 pure pure ADJ iajs-1988 148 11 & & CCONJ iajs-1988 148 12 appl.sci appl.sci PROPN iajs-1988 148 13 . . PUNCT iajs-1988 148 14 ihjpas ihjpas PROPN iajs-1988 148 15 https://doi.org/10.30526/32.1.1988 https://doi.org/10.30526/32.1.1988 DET iajs-1988 148 16 vol vol NOUN iajs-1988 148 17 . . PUNCT iajs-1988 149 1 32 32 NUM iajs-1988 149 2 ( ( PUNCT iajs-1988 149 3 1 1 NUM iajs-1988 149 4 ) ) PUNCT iajs-1988 149 5 2019 2019 NUM iajs-1988 149 6 9 9 NUM iajs-1988 149 7 . . PUNCT iajs-1988 150 1 choudhury choudhury PROPN iajs-1988 150 2 , , PUNCT iajs-1988 150 3 s. s. PROPN iajs-1988 150 4 ; ; PUNCT iajs-1988 150 5 karapinar karapinar PROPN iajs-1988 150 6 , , PUNCT iajs-1988 150 7 e. e. PROPN iajs-1988 150 8 ; ; PUNCT iajs-1988 150 9 kundu kundu NOUN iajs-1988 150 10 , , PUNCT iajs-1988 150 11 a.tripled a.triple VERB iajs-1988 150 12 coincidence coincidence NOUN iajs-1988 150 13 point point NOUN iajs-1988 150 14 theorems theorem NOUN iajs-1988 150 15 for for ADP iajs-1988 150 16 nonlinear nonlinear ADJ iajs-1988 150 17 contractions contraction NOUN iajs-1988 150 18 in in ADP iajs-1988 150 19 partially partially ADV iajs-1988 150 20 ordered order VERB iajs-1988 150 21 metric metric ADJ iajs-1988 150 22 space space NOUN iajs-1988 150 23 . . PUNCT iajs-1988 151 1 int int NOUN iajs-1988 151 2 . . PUNCT iajs-1988 152 1 journal journal PROPN iajs-1988 152 2 of of ADP iajs-1988 152 3 math math NOUN iajs-1988 152 4 and and CCONJ iajs-1988 152 5 math math NOUN iajs-1988 152 6 . . PUNCT iajs-1988 153 1 sciences science NOUN iajs-1988 153 2 . . PUNCT iajs-1988 153 3 2012 2012 NUM iajs-1988 153 4 , , PUNCT iajs-1988 153 5 201 201 NUM iajs-1988 153 6 , , PUNCT iajs-1988 153 7 14 14 NUM iajs-1988 153 8 pages page NOUN iajs-1988 153 9 . . PUNCT iajs-1988 154 1 10 10 NUM iajs-1988 154 2 . . PUNCT iajs-1988 155 1 imdad imdad PROPN iajs-1988 155 2 , , PUNCT iajs-1988 155 3 m. m. NOUN iajs-1988 155 4 ; ; PUNCT iajs-1988 155 5 soliman soliman NOUN iajs-1988 155 6 , , PUNCT iajs-1988 155 7 a. a. PROPN iajs-1988 155 8 ; ; PUNCT iajs-1988 155 9 choudhary choudhary PROPN iajs-1988 155 10 , , PUNCT iajs-1988 155 11 s. s. PROPN iajs-1988 155 12 ; ; PUNCT iajs-1988 155 13 das das PROPN iajs-1988 155 14 , , PUNCT iajs-1988 155 15 p. p. NOUN iajs-1988 155 16 on on ADP iajs-1988 155 17 n n CCONJ iajs-1988 155 18 - - PUNCT iajs-1988 155 19 tupled tuple VERB iajs-1988 155 20 coincidence coincidence NOUN iajs-1988 155 21 point point NOUN iajs-1988 155 22 results result NOUN iajs-1988 155 23 in in ADP iajs-1988 155 24 metric metric ADJ iajs-1988 155 25 spaces space NOUN iajs-1988 155 26 . . PUNCT iajs-1988 156 1 journal journal NOUN iajs-1988 156 2 of of ADP iajs-1988 156 3 operators operator NOUN iajs-1988 156 4 . . PUNCT iajs-1988 157 1 2013 2013 NUM iajs-1988 157 2 , , PUNCT iajs-1988 157 3 2013 2013 NUM iajs-1988 157 4 , , PUNCT iajs-1988 157 5 8 8 NUM iajs-1988 157 6 pages page NOUN iajs-1988 157 7 . . PUNCT