item: #1 of 431 id: agt-10036 author: Dahane, Intissar; Dridi, Lobna; Lazaar, Sami title: F-n-resolvable spaces and compactifications date: 2019-04-01 words: 5112 flesch: 79 summary: Keywords: categories; functors; resolvable spaces; compactifications. Generalizing the concept of resolvable spaces introduced by Hewitt in [16], Ceder in [6] defined a topological space X to be n-resolvable space if it has a family of n pairwise disjoints dense subsets. keywords: space; subset cache: agt-10036.pdf plain text: agt-10036.txt item: #2 of 431 id: agt-10129 author: Liu, Yang title: Structure of symmetry group of some composite links and some applications date: 2020-10-01 words: 2559 flesch: 78 summary: Gen. Topol. 21, no. 2 (2020), 171-176 doi:10.4995/agt.2020.10129 c© AGT, UPV, 2020 Structure of symmetry group of some composite links and some applications Yang Liu∗ Shenzhen Technology University, Shenzhen, China (liuyang2@sztu.edu.cn) Keywords: knot; link; geometric topology; symmetry group; classification of links. keywords: group; symmetry cache: agt-10129.pdf plain text: agt-10129.txt item: #3 of 431 id: agt-10171 author: Bag, Sagarmoy; Acharyya, Sudip Kumar; Mandal, Dhananjoy title: A class of ideals in intermediate rings of continuous functions date: 2019-04-01 words: 4419 flesch: 80 summary: It is realized that a P-space X is discrete if and only if C(X) is identical to the ring of real valued measurable functions defined on the σ-algebra β(X) of all Borel sets in X. Interrelation between z-ideals, z◦-ideal and ZA-ideals in A(X) are examined. To achieve that we have chosen three special classes of ideals z-ideals, z◦-ideals and ZA-ideals in a typical intermediate ring A(X). keywords: a(x; ideal cache: agt-10171.pdf plain text: agt-10171.txt item: #4 of 431 id: agt-10213 author: Belbaki, Rabah; Karapinar, Erdal; Ould-Hammouda,, Amar title: On Reich type λ−α-nonexpansive mapping in Banach spaces with applications to L1([0,1]) date: 2018-10-04 words: 5685 flesch: 83 summary: Since z ∈ K fixed point, 0 = λ‖z −T (z)‖≤‖z −x‖ , we have ‖z −T (x)‖≤ α‖z −T (x)‖+ α‖T We say that a mapping T : K → K satisfies (C)-condition on K if for x, y ∈ K we have 1 2 ‖x−T (x)‖≤‖x−y‖⇒‖T (x)−T (y)‖≤‖x−y‖. It is clear that each nonexpansive mapping satisfies the condition (C) but the converse is not true. keywords: mapping cache: agt-10213.pdf plain text: agt-10213.txt item: #5 of 431 id: agt-10360 author: Radhakrishnan, M.; Rajesh, S. title: Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings date: 2019-04-01 words: 6428 flesch: 85 summary: If for each x ∈ K, the following inequality holds lim sup n→∞ ( sup y∈K {‖T nx − T ny‖ − ‖x − y‖} ) ≤ 0, then T is said to be asymptotically nonexpansive type. − T n x0‖ ≤ N(X)δ(D1). keywords: banach; lim; sup cache: agt-10360.pdf plain text: agt-10360.txt item: #6 of 431 id: agt-10474 author: Boxer, Laurence; Staecker, P. Christopher title: Remarks on fixed point assertions in digital topology date: 2019-04-01 words: 9049 flesch: 76 summary: Digital fixed points and approximate fixed points. [7] L. Boxer, O. Ege, I. Karaca, J. Lopez and J. Louwsma, Digital fixed points, approximate fixed points, and universal functions, Applied General Topology 17, no. 2 (2016), 159– 172. keywords: contraction; digital; map; metric; point; theorem cache: agt-10474.pdf plain text: agt-10474.txt item: #7 of 431 id: agt-10490 author: Rath, N. title: Cauchy action on filter spaces date: 2019-04-01 words: 7982 flesch: 84 summary: [{F ∩ G | F ∈ F, G ∈ G}]. [{F ∪ G | F ∈ F, G ∈ G}]. keywords: action; cauchy; filter; group; space cache: agt-10490.pdf plain text: agt-10490.txt item: #8 of 431 id: agt-10635 author: Izuchukwu, C.; Aremu, K. O.; Mebawondu, A. A.; Mewomo, O. T. title: A viscosity iterative technique for equilibrium and fixed point problems in a Hadamard space date: 2019-04-01 words: 8225 flesch: 84 summary: (ii) d2(tx ⊕ (1 − t)y, z) ≤ td2(x, z) + (1 − t)d2(y, z) − t(1 − t)d2(x, y) (see [13]). Then, for all x, y ∈ X, (1) 〈−→utx, −→ uty〉 ≤ t〈 −→ ux, −→ uty〉 + (1 − t)〈 −→ vx, −→ uty〉; (2) 〈−→utx, −→ uy〉 ≤ t〈−→ux, −→uy〉 + (1 − t)〈−→vx, −→ux〉 and (3) 〈−→utx, −→ vy〉 ≤ t〈−→ux, −→vy〉 + (1 − t)〈−→vx, −→vy〉. keywords: point; space cache: agt-10635.pdf plain text: agt-10635.txt item: #9 of 431 id: agt-10667 author: Boxer, Laurence title: Remarks on fixed point assertions in digital topology, 2 date: 2019-04-01 words: 8729 flesch: 84 summary: If d is a metric on a digital image (X,κ) such that for all distinct x,y ∈ X we have d(x,y) > If d is a metric on (X,κ) such that for all distinct x,y ∈ X we have d(x,y) > a for some constant a > 0, then any Cauchy sequence in X is eventually constant, and (X,d) is a complete metric space. keywords: metric; point; space cache: agt-10667.pdf plain text: agt-10667.txt item: #10 of 431 id: agt-10714 author: Bella, Angelo; Hernández-Gutiérrez, Rodrigo title: A non-discrete space X with Cp(X) Menger at infinity date: 2019-04-01 words: 3824 flesch: 82 summary: According to [5, Theorem 3.5], Menger filters are precisely those called Can- jar filters. If a space is the countable union of Menger spaces, then it is Menger as well. keywords: filter; infinity; menger cache: agt-10714.pdf plain text: agt-10714.txt item: #11 of 431 id: agt-10731 author: Ghasemzadeh, S.; Namdari, M. title: When is the super socle of C(X) prime? date: 2019-04-01 words: 2787 flesch: 80 summary: Let X be a zero-dimensional cocountably-disconnected space, with X \ Ic(X) a singleton and f(Ic(X)) An element p ∈ X is called a countably isolated point if p has a countable neighborhood. keywords: c(x; scf cache: agt-10731.pdf plain text: agt-10731.txt item: #12 of 431 id: agt-10776 author: Deb Ray, A.; Mondal, Atanu title: On rings of Baire one functions date: 2019-04-01 words: 6111 flesch: 87 summary: For a normal space X, f ∈ B1(X) is a unit in B1(X) if and only if Z(f) = {x ∈ X : f(x) = 0} = ∅. Proof. If f ∈ B1(X) is a unit then clearly the condition holds. keywords: b1(x; baire; functions cache: agt-10776.pdf plain text: agt-10776.txt item: #13 of 431 id: agt-10928 author: Marinelli, K.; Peters, T. J. title: Exact computation for existence of a knot counterexample date: 2019-04-01 words: 4568 flesch: 68 summary: Communicated by M. Schellekens Abstract Previously, numerical evidence was presented of a self-intersecting Bézier curve having the unknot for its control polygon. Bézier curves are shown to have differing prime knot types, so there must be an intermediate Bézier curve with a self-intersection (as shown in the middle image by a black dot). keywords: bézier; control; curve; peters; point; polygon; subdivision cache: agt-10928.pdf plain text: agt-10928.txt item: #14 of 431 id: agt-10930 author: García Macias, Gonzalo title: A quantitative version of the Arzelà-Ascoli theorem based on the degree of nondensifiability and applications date: 2019-04-01 words: 6422 flesch: 84 summary: Let B ∈ BC(I,X) be equicontinuous. By Proposition 2.4, we can assume without loss of generality that θ ∈ B, θ being the null vector of ℓ2. keywords: theorem cache: agt-10930.pdf plain text: agt-10930.txt item: #15 of 431 id: agt-11065 author: Vidal-Escobar, Ivon; Garcia-Ferreira, Salvador title: The function ω ƒ on simple n-ods date: 2019-10-01 words: 12592 flesch: 96 summary: y ∈ y ∈ [b,f(v)]. keywords: fix(f; function cache: agt-11065.pdf plain text: agt-11065.txt item: #16 of 431 id: agt-11117 author: Boxer, Laurence title: Remarks on fixed point assertions in digital topology, 3 date: 2019-10-01 words: 5165 flesch: 82 summary: If there exist x0,y0 ∈ X such that either • d(x0,y0) = diamX > 0, or • d(x0,y0) = min{d(x,y) |x,y ∈ X,x 6= y}, then there is no self-map T : Since X is finite or d is an `p metric, there exist x0,y0 ∈ X such that m = d(x0,y0) = min{d(x,y) |x,y ∈ X,x 6= y} > 0. keywords: digital; point cache: agt-11117.pdf plain text: agt-11117.txt item: #17 of 431 id: agt-11238 author: Pal, Sudip Kumar; Adhikary, Nayan; Samanta, Upasana title: On ideal sequence covering maps date: 2019-10-01 words: 8132 flesch: 87 summary: Then {yi,n}, J -converging to yi in Yi for i = 1, 2, · · · ,N. Now there is a sequence {xi,k}, I-converging to xi such that fi(xi,k) = yi,nk, k ∈ N and {n ∈ N : xi,k 6∈ f −1 i (yi,n) for all k ∈ N} ∈ L for i = 1, 2, · · · ,N, . Then for each non-isolated point y ∈ Y, there is a point xy ∈ ∂f−1(y) such that whenever U is an open subset with xy ∈ U, there exists a P ∈Py satisfying P ⊂ f(U). keywords: covering; map; sequence cache: agt-11238.pdf plain text: agt-11238.txt item: #18 of 431 id: agt-11260 author: Protasov, Igor V. title: Extremal balleans date: 2019-04-01 words: 4322 flesch: 89 summary: E−1 = {(y, x) : (x, y) ∈ E}; • if E ∈ E and △X ⊆ E ′ ⊆ E then E′ ∈ E; • for any x, y ∈ X, there exists E ∈ E such that (x, y) ∈ E. Received 20 January 2019 – Accepted 21 February 2019 A subset Y is called bounded if Y ⊆ E[x] for some x ∈ X and E ∈ E. Given a ballean (X, E), a subset Y of X is called • large if there exists E ∈ E such that X = E[A]; • small if (X \ A) ∩ L is large for each large subset L; • thick if, for every E ∈ E, there exists a ∈ A such that E[a] ⊆ A. keywords: ballean cache: agt-11260.pdf plain text: agt-11260.txt item: #19 of 431 id: agt-11368 author: Babaei, Reza; Rahimi, Hamidreza; Soleimani Rad, Ghasem title: Fixed point results with respect to a wt-distance in partially ordered b-metric spaces and its application to nonlinear fourth-order differential equation date: 2022-04-01 words: 5768 flesch: 88 summary: x = y for all x,y ∈ X; (iv) pre-order if it is reflexive and transitive. Since ρ(x,y) = d(x,y) for all x,y ∈ X, by passing to square and taking the supremum with respect to t, we get ρ(fx,fy) = d(fx,fy) = sup t∈[0,1] ((fy)(t) − (fx)(t))2 ≤ α1(x)ρ(x,y) for all x,y ∈ X with y v x. keywords: fixed; metric cache: agt-11368.pdf plain text: agt-11368.txt item: #20 of 431 id: agt-11369 author: Dinarvand, Mina title: Fixed points for fuzzy quasi-contractions in fuzzy metric spaces endowed with a graph date: 2020-10-01 words: 9363 flesch: 83 summary: Suppose that (X, M, !) is a fuzzy metric space endowed with a graph G and T : X → X is a G-fuzzy H-Banach contraction with respect to η ∈ H in the sense that T preserves the edges of G and there exists α ∈ (0, 1) such that η # M(Tx, Ty, t) $ ≤ αη # M(x, y, t) $ for all x, y ∈ X with (x, y) ∈ E(G) and any t > 0. It is worth mentioning that if η ∈ H, then η(1) = 0 and η is continuous. keywords: fuzzy; metric; η ∈ cache: agt-11369.pdf plain text: agt-11369.txt item: #21 of 431 id: agt-11417 author: Deb Ray, A.; Mondal, Atanu title: Ideals in B1(X) and residue class rings of B1(X) modulo an ideal date: 2019-10-01 words: 7390 flesch: 92 summary: [ZB[I]] = I, i.e., ∀ f ∈ B1(X), f ∈ I ⇐⇒ Z(f) ∈ ZB[I]. I} = {f ∈ B1(X) : keywords: b1(x; ideal; theorem cache: agt-11417.pdf plain text: agt-11417.txt item: #22 of 431 id: agt-11524 author: Veisi, Amir title: ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X) date: 2019-10-01 words: 5774 flesch: 89 summary: f ∈ Cc(X)} and Z∗c (X) = {Z(g) : In [5], a Huasdorff space X is called countably completely regular (briefly, c- completely regular) if whenever F is a closed subset of X and x /∈ F, there exists f ∈ Cc(X) such that f(x) = 0 and f(F) keywords: ideal cache: agt-11524.pdf plain text: agt-11524.txt item: #23 of 431 id: agt-11541 author: Sharma, Puneet; Kumar, Dileep title: Matrix characterization of multidimensional subshifts of finite type date: 2019-10-01 words: 6086 flesch: 64 summary: 2010 MSC: 37B10; 37B20; 37B50. Keywords: multidimensional shift spaces; shifts of finite type; periodicity in multidimensional shifts of finite type. While [1] investigated mixing properties of multidimensional shift of finite type, [2] investigated minimal forbidden patterns for multidimensional shift spaces. keywords: finite; matrix; set; shift; shift space; space cache: agt-11541.pdf plain text: agt-11541.txt item: #24 of 431 id: agt-11605 author: Bouziad, Ahmed title: On proximal fineness of topological groups in their right uniformity date: 2019-10-01 words: 6731 flesch: 81 summary: For g ∈ G, let ψg : G → Y be the function defined by ψg(h) = f(gh). For every x ∈ X and g ∈ G, there is U ∈ V(e) such that f(Ugx) ⊂ V [f(gx)]. keywords: group cache: agt-11605.pdf plain text: agt-11605.txt item: #25 of 431 id: agt-11645 author: Dikranjan, Dikran; Protasov, Igor V.; Protasova, Ksenia; Zava, Nicolò title: Balleans, hyperballeans and ideals date: 2019-10-01 words: 8122 flesch: 84 summary: α ∈ P ; (ii) symmetry, i.e., for any α ∈ P and every pair of points x,y ∈ X, x ∈ B(y,α) if and only if y ∈ B(x,α); Received 13 May 2018 – Accepted 15 July 2018 A ballean B is called connected if, for any x,y ∈ X, there exists α ∈ P such that y ∈ B(x,α). keywords: ary; ballean cache: agt-11645.pdf plain text: agt-11645.txt item: #26 of 431 id: agt-11683 author: Tabassum, Rehana; Azam, Akbar; Mohammed, Shehu Shagari title: Existence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle date: 2019-10-01 words: 8159 flesch: 81 summary: = γ } = [ 0,u− u2 2 ] and [G (u)](T ,N,δ) = { t ∈ U : T ( µG(u) N and ξ = n for ξ ∈ N. Notice that for ξ = n ∈ N, problems (4.1)-(4.2) are reduced to classical Cauchy problem for the ordinary differential equation. keywords: set cache: agt-11683.pdf plain text: agt-11683.txt item: #27 of 431 id: agt-11807 author: Barragán, Franco; Santiago-Santos, Alicia; Tenorio, Jesús F. title: Dynamic properties of the dynamical system SFnm(X), SFnm(f)) date: 2020-04-03 words: 8190 flesch: 86 summary: Given x ∈ X, the orbit of x under f is the set O(x,f) = {fk(x) | A point p ∈ X is a periodic point in (X,f) provided that there exists k ∈ N such that fk(p) = p. keywords: m(f; mixing; sfnm(x),sf; system cache: agt-11807.pdf plain text: agt-11807.txt item: #28 of 431 id: agt-11865 author: Zaitov, Adilbek Atakhanovich title: On a metric of the space of idempotent probability measures date: 2020-04-03 words: 7206 flesch: 82 summary: For every pair of Dirac measures δx, δy, x, y ∈ X, the uniqueness of a coupling ξ ∈ I(X2) of δx and δy, ξ = 0 � δ(x,y), implies that ρ1(δx, δy) = ξ(ρ) ⊕ρ(x, y) = 0 � δ(x,y)(ρ) ⊕ρ(x, y) = ρ(x, y). Let (X, ρ) be a metric space, x, y ∈ X be points such that ρ(x, y) = keywords: i(x; measures; probability; space cache: agt-11865.pdf plain text: agt-11865.txt item: #29 of 431 id: agt-11902 author: Ullah, Kifayat; Ahmad, Junaid; Khan, Fida Muhammad title: Numerical reckoning fixed points via new faster iteration process date: 2022-04-01 words: 3812 flesch: 82 summary: A mapping T : M → M is said to generalized α-nonexpansive if there exists a real number α ∈ [0, 1) such that for each x,y ∈ M, 1 2 ||x−Tx|| ≤ ||x−y|| ⇒ ||Tx−Ty|| ≤ α||Tx−y||+α||Ty−x||+(1−2α)||x−y||. Then for each x,y ∈ M, ||x−Ty|| ≤ ( 3 + α 1 −α ) ||x−Tx|| + ||x−y||. (v) If X has Opial property, T is generalized α-nonexpansive, {xn} con- verges weakly to a point v and limn→∞ ||Txn−xn|| = 0, then v ∈ F(T). keywords: nonexpansive; −p|| cache: agt-11902.pdf plain text: agt-11902.txt item: #30 of 431 id: agt-11903 author: Kharbhih, John Paul Jala; Dutta, Sanghita title: Closure formula for ideals in intermediate rings date: 2020-10-01 words: 2707 flesch: 92 summary: Now, the collection {Σp : p ∈ βX − Ω} forms an open cover for the compact set βX = 1. Let Ω = {p ∈ βX : hβ(p) < 1}. keywords: a(x; ideal cache: agt-11903.pdf plain text: agt-11903.txt item: #31 of 431 id: agt-11992 author: Garg, Medha; Chandok, Sumit title: Existence of Picard operator and iterated function system date: 2020-04-03 words: 5768 flesch: 89 summary: Now as (M,d) is a complete metric space so there exist u ∈ M such that {un} converges to u. From (Θ1) and (3.1), it is easy to conclude that θ(d(fu,fv)) Now as (M,d) is a complete metric space so there exist u ∈ M such that {un} converges to u. The continuity of f and uniqueness of limit implies fu = u, thus we get a fixed point. keywords: k(m cache: agt-11992.pdf plain text: agt-11992.txt item: #32 of 431 id: agt-12042 author: Abuzaid, Dina; Alqahtani, Maha; Kalantan, Lutfi title: New topologies between the usual and Niemytzki date: 2020-04-03 words: 4612 flesch: 83 summary: For every 〈x,y〉 ∈ X and r > 0, let Ur(〈x,y〉) be the set of all points of X inside the circle of radius r and centered at 〈x,y〉. 〈x,y〉 ∈ X} by B. Let W = {X \G : G ∈ B}. keywords: uan cache: agt-12042.pdf plain text: agt-12042.txt item: #33 of 431 id: agt-12065 author: Bella, Angelo; Spadaro, Santi title: A note on rank 2 diagonals date: 2020-04-03 words: 2146 flesch: 74 summary: Gen. Topol. 21, no. 1 83 A. Bella and S. Spadaro Related results for the classes of dually ccc spaces and for that of cellular- Lindelöf spaces were proved in [16] and [7] R. Buzyakova, Cardinalities of ccc spaces with regular Gδ-diagonals, Topology Appl. keywords: rank; space cache: agt-12065.pdf plain text: agt-12065.txt item: #34 of 431 id: agt-12091 author: Boxer, Laurence; Staecker, P. Christopher title: Fixed point sets in digital topology, 1 date: 2020-04-03 words: 10518 flesch: 86 summary: We introduce several measures related to fixed points for continuous self-maps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum F(X) of a digital image: that is, the set of all numbers that can appear as the num- ber of fixed points for some continuous self-map. keywords: f(x; fix(f; image; map; points; theorem cache: agt-12091.pdf plain text: agt-12091.txt item: #35 of 431 id: agt-12101 author: Boxer, Laurence title: Fixed point sets in digital topology, 2 date: 2020-04-03 words: 10401 flesch: 89 summary: � Given a digital image (X,κ) and f ∈ C(X,κ), a point x ∈ X is an almost fixed point of f Suppose y ∈ X is such that y ↔c1 (0, 0). keywords: digital; f(x; freezing; point; set cache: agt-12101.pdf plain text: agt-12101.txt item: #36 of 431 id: agt-12220 author: Okeke, Godwin Amechi; Abbas, Mujahid title: Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces date: 2020-04-03 words: 9780 flesch: 81 summary: Recently, Okeke [32] exploited the idea of complex valued metric spaces to define the concept of complex valued Banach spaces and then initiated the idea of approximating the fixed point of nonlinear mappings in complex valued Banach spaces. The notion of complex valued metric spaces was introduced by Azam et al. keywords: banach; complex; cone; metric; point; results; spaces; −p‖ cache: agt-12220.pdf plain text: agt-12220.txt item: #37 of 431 id: agt-12238 author: Khan, Moiz ud Din; Sabah, Amani title: Selection principles and covering properties in bitopological spaces date: 2020-04-03 words: 5881 flesch: 82 summary: (6) p-Rothberger if for each sequence (Un : n ∈ N) of p-open covers of X, there is a sequence (Un : n ∈ N) such that for every n ∈ N, Un∈Un and {Un : n ∈ N} is a p-open cover of X. (7) p-Hurewicz (or simply pairwise Hurewicz), if it satisfies: For each se- quence (Un : n ∈ N) of elements of p-O, there is a sequence (Vn : n ∈ N) such that for each n ∈ N, Vn is a finite subset of Un, and for each x ∈ X, for all but finitely many n, x ∈∪Vn. Then there exists a sequence (Vn : n ∈ N) such that for every n ∈ N, Vn is a finite subset of U′n and each x ∈ X belongs to ∪Vn for all but finitely many n. By construction, for each n ∈ N and V ∈Vn there exists UV ∈ Un such that V = Cli(UV ). keywords: open; sequence; ∈ n cache: agt-12238.pdf plain text: agt-12238.txt item: #38 of 431 id: agt-12258 author: Bardyla, Serhii; Ravsky, Alex title: Closed subsets of compact-like topological spaces date: 2020-10-01 words: 7282 flesch: 75 summary: We prove this lemma for the case of topological semigroups X and Y . According to Tychonoff’s theorem, a (Tychonoff) product of a family of compact spaces is compact, On the other hand, there are two countably com- pact spaces whose product is not feebly compact (see [10], the paragraph before Theorem 3.10.16). keywords: semigroup; space cache: agt-12258.pdf plain text: agt-12258.txt item: #39 of 431 id: agt-12929 author: Ali Akbar, Kamaludheen title: The class of simple dynamics systems date: 2020-10-01 words: 8685 flesch: 80 summary: For every closed subset F of R there exist continuous maps f : R → R and g : R → R such that S(f) = Fix(g) Conversely, for every closed subset F of R there exist continuous maps f, g : R → R such that S(f) = Fix(g) keywords: conjugacy; maps; order; points cache: agt-12929.pdf plain text: agt-12929.txt item: #40 of 431 id: agt-13066 author: Deng, Jialong title: Metric topology on the moduli space date: 2021-04-01 words: 1735 flesch: 76 summary: A map f : X → Y is called an ε-isometry between compact metric spaces X and Y , if |dX(a, b) − dY (f(a), f(b))| ≤ ε for all a, b ∈ X. Definition 2.2 (ε-distance). Usually those four metrics are not complete metrics on M(M), so M(M) is local compact topology spaces endowed with their induced metric topology in general. keywords: m(m; metric; topology cache: agt-13066.pdf plain text: agt-13066.txt item: #41 of 431 id: agt-13075 author: Boxer, Laurence title: Remarks on fixed point assertions in digital topology, 4 date: 2020-10-01 words: 8478 flesch: 81 summary: Then for all x, y ∈ X, d(Sx, Sy) ≤ µd(Tx, Ty). ≤ αd(T(x), T(y)) for all x, y ∈ X, then T and S have a common fixed point. keywords: digital; let cache: agt-13075.pdf plain text: agt-13075.txt item: #42 of 431 id: agt-13084 author: Sabao, Hope; Otafudu, Olivier Olela title: On soft quasi-pseudometric spaces date: 2021-04-01 words: 6085 flesch: 86 summary: In this article, we introduce soft quasi-pseudometric spaces, a concept that generalise soft metric spaces to the asymmetric setting. 22, no. 1 (2021), 17-30doi:10.4995/agt.2021.13084 © AGT, UPV, 2021 On soft quasi-pseudometric spaces Hope Sabao a and Olivier Olela Otafudu b a School of Mathematics, University of the Witwatersrand Johannesburg 2050 , South Africa. keywords: u y; ∼ u cache: agt-13084.pdf plain text: agt-13084.txt item: #43 of 431 id: agt-13126 author: Sun, Taixiang; Li, Lue; Su, Guangwang; Han, Caihong; Xia, Guoen title: The depth and the attracting centre for a continuous map on a fuzzy metric interval date: 2020-10-01 words: 5144 flesch: 95 summary: y ∈ I × (0, ∞) −→ [0, 1] such that for any x, y ∈ I and t > 0, Md(x, y, t) = t t + |x − y| . keywords: metric cache: agt-13126.pdf plain text: agt-13126.txt item: #44 of 431 id: agt-13148 author: Temel, Sedat title: Further remarks on group-2-groupoids date: 2021-04-01 words: 6845 flesch: 83 summary: The actions of G0 on Ker(sh) and on Ker(s) are drawn in the following diagram: e x•f ++ x•g 33 ✤✤ ✤✤ �� x•α xyx −1 := x 1x (( 1x 66 ✤✤ ✤✤ �� 11x x · e f (( g 66 ✤✤ ✤✤ �� α y · x −1 1−1x ** 1−1x 44 ✤✤ ✤✤ �� 1 −1 1x x−1 We denote the category of such internal groupoids in Cm by IGCm. Crossed modules over group-groupoids In this section, we work on crossed modules over groupoids by replacing such groupoids with group-groupoids. keywords: groupoids; ✤ ✤; ✤ � cache: agt-13148.pdf plain text: agt-13148.txt item: #45 of 431 id: agt-13154 author: Staecker, P. Christopher title: Digital homotopy relations and digital homology theories date: 2021-10-01 words: 12969 flesch: 78 summary: [6] O. Ege and I. Karaca, Fundamental properties of digital simplicial homology groups, American Journal of Computer Technology and Application 1 (2013), 25–41. [9] S. S. Jamil and D. Ali, Digital Hurewicz theorem and digital homology theory, arxiv eprint 1902.02274v3. keywords: adjacency; cubical; digital; homology; homotopy; image; theorem cache: agt-13154.pdf plain text: agt-13154.txt item: #46 of 431 id: agt-13156 author: Altassan, Alaa; Alharbi, Nof; Aydi, Hassen; Özel, Cenap title: Rough action on topological rough groups date: 2020-10-01 words: 4400 flesch: 77 summary: Gen. Topol. 21, no. 2 (2020), 295-304 doi:10.4995/agt.2020.13156 c© AGT, UPV, 2020 Rough action on topological rough groups Alaa Altassan a, Nof Alharbi a, Hassen Aydi b,c, Cenap Özel a a Department of Mathematics, King Abdulaziz University, Jeddah, Kingdom of Saudi Ara- bia (aaltassan@kau.edu.sa,nof20081900@hotmail.com,cozel@kau.edu.sa) b Université de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia. Next, we combine these two notions in order to define topological rough homogeneous spaces, discussing results concerning open subsets in topological rough groups. keywords: group; set cache: agt-13156.pdf plain text: agt-13156.txt item: #47 of 431 id: agt-13165 author: Acharyya, Amrita; Acharyya, Sudip Kumar; Bag, Sagarmoy; Sack, Joshua title: Intermediate rings of complex-valued continuous functions date: 2021-04-01 words: 10686 flesch: 84 summary: ∈ C ∗(X,C) Since h1 ∈ C ∗(X,C), it follows that f1,g1 ∈ C ∗(X). keywords: a(x; c(x; ideal; p(x; ring; theorem; σ(x cache: agt-13165.pdf plain text: agt-13165.txt item: #48 of 431 id: agt-13225 author: Rashedi, Fatemeh title: A new topology over the primary-like spectrum of a module date: 2021-10-01 words: 3363 flesch: 84 summary: By a prime submodule (or a p-prime submodule) of M, we mean a proper submodule P with p = (P : M) such that rm ∈ P for r ∈ R and m ∈ M implies that either m ∈ P or r ∈ p. Suppose M is a p-module and R/Ann(M) has ACC on ideals. keywords: topology cache: agt-13225.pdf plain text: agt-13225.txt item: #49 of 431 id: agt-13248 author: Georgiev Georgiev, Svetlin; Mebarki, Karima title: On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs date: 2021-10-01 words: 10778 flesch: 96 summary: − t1)4(x − x1)4g(t1, x1)dx1dt1 +r ∫ t 0 ∫ x 0 x21(t t1 0 ∫ x1 0 (x1 − x2)β(t2) ×|u(t2, x2)|dx2dt2dx1dt1 −12 ∫ t 0 ∫ x 0 (t − t1)4(x − x1)g(t1, x1) ∫ keywords: − t1)4(x; ∫ t; ∫ t1; ∫ x1 cache: agt-13248.pdf plain text: agt-13248.txt item: #50 of 431 id: agt-13446 author: Salem, Aymen Haj; Hattab, Hawete; Rejeiba, Tarek title: Equicontinuous local dendrite maps date: 2021-04-01 words: 4916 flesch: 83 summary: Con- versely, given x ∈ ⋂ n∈N fn(X), there is a sequence xk ∈ X and x0 ∈ X with xk → x0 and nk → +∞ such that f nk(xk) = x for all If f is not equicontinuous, then there exist x ∈ X, a sequence (xn)n in X with xn → x and a sequence (pn)n in N, © AGT, UPV, 2021 Appl. keywords: dendrite; ω(x cache: agt-13446.pdf plain text: agt-13446.txt item: #51 of 431 id: agt-13553 author: İs, Melih; Karaca, Ismet title: The higher topological complexity in digital images date: 2020-10-01 words: 9933 flesch: 78 summary: Let α∗ be the adjacency relation on the cartesian product digital image X × [0, n]Z −→ Y are digital maps such that g(a) = G(a, 0) for a ∈ İ. Define a digital map k : İm × keywords: complexity; digital; images; m]z; map cache: agt-13553.pdf plain text: agt-13553.txt item: #52 of 431 id: agt-13608 author: Mitra, Biswajit; Chowdhury, Debojyoti title: Ideal spaces date: 2021-04-01 words: 5253 flesch: 80 summary: They further proved that within the class of local compact spaces, the no- tions of ideal space and pseudocompact space are identical. At the end we tried to explore few topological properties of ideal spaces and finally have shown that if Xand Y are nearly pseudocompact, then X × Y is nearly pseudocompact if and only if X × Y is ideal space. keywords: ideal; pseudocompact; space; theorem cache: agt-13608.pdf plain text: agt-13608.txt item: #53 of 431 id: agt-13640 author: Spreen, Dieter title: On domains witnessing increase in information date: 2000-10-01 words: 11218 flesch: 82 summary: Because of our choice of zm�1 (1) and (2) then also hold for z0; : : : ;zm�1. ForProperty (3) we only have to show that for all j < m � 1, zj � zm�1. Let I be an index set with at least two members and �Di�i2I be a family ofdomains. keywords: domains; information; k(d; nite; scott; set; tr(f cache: agt-13640.pdf plain text: agt-13640.txt item: #54 of 431 id: agt-13696 author: Acharyya, Sudip Kumar; Bharati, Rakesh; Deb Ray, Atasi title: Intrinsic characterizations of C-realcompact spaces date: 2021-10-01 words: 4175 flesch: 77 summary: In the present article we offer a new characterization of c- realcompact spaces on using the notion, c-stable family of closed sets in X. A family F of subsets of X is called c-stable if given f ∈ C(X,Z), there exists F ∈ F such that f is bounded on F . For a maximal ideal M in Cc(X) and for f ∈ Cc(X), |M(f)| is infinitely large in Cc(X)/M if and only if f is unbounded on every zero set of Zc(M) keywords: realcompact; space cache: agt-13696.pdf plain text: agt-13696.txt item: #55 of 431 id: agt-13836 author: Bella, Angelo; Hrusak, Michael title: A disjointly tight irresolvable space date: 2020-10-01 words: 1410 flesch: 76 summary: However, every countable maximal space is homeomorphic to a subspace of 2c and, consistently, there are maximal spaces which are embedable into 2κ for some κ < c. Problem 1.5. Following [2] we say that a space X is disjointly tight (or it has disjoint tightness) if whenever x ∈ X is an accumulation point of a set keywords: space; tightness cache: agt-13836.pdf plain text: agt-13836.txt item: #56 of 431 id: agt-13902 author: Lael, Fatemeh; Shabanian, Samira title: Convexity and boundedness relaxation for fixed point theorems in modular spaces date: 2021-04-01 words: 7691 flesch: 83 summary: − y),ρ(x − z),ρ(y − w),ρ(x − w),ρ(y − z)}, where 2kwρ(2) < − y),αρ(x − z),αρ(y − w), β 2 (ρ(x − w) keywords: fixed; metric; modular; point; spaces cache: agt-13902.pdf plain text: agt-13902.txt item: #57 of 431 id: agt-13926 author: Fouladi, Farhad; Abkar, Ali; Karapinar, Erdal title: Weak proximal normal structure and coincidence quasi-best proximity points date: 2020-10-01 words: 6592 flesch: 88 summary: sup{‖x − y‖ : x ∈ A, y ∈ B}; δ(x, B) = sup{‖x − y‖ : y ∈ B}. keywords: dist(s(a; pair; s(b; s(k2 cache: agt-13926.pdf plain text: agt-13926.txt item: #58 of 431 id: agt-13943 author: Bisht, Ravindra K.; Rakocevic, Vladimir title: Discontinuity at fixed point and metric completeness date: 2020-10-01 words: 6230 flesch: 84 summary: Fixed point theorems studied by Kannan are considered as the genesis of the question on continuity of contractive mappings at the fixed point (see [15, 16]). Fixed point theorems for discontinuous mappings have found a variety of applications, e.g., neural networks are generally used in character recognition, image compression, stock market prediction and to solve non-negative sparse approximation problems ([10, 11, 20, 21, 22, 38]). keywords: fixed; point cache: agt-13943.pdf plain text: agt-13943.txt item: #59 of 431 id: agt-14000 author: Gabeleh, Moosa; Patle, Pradip Ramesh title: Best proximity point (pair) results via MNC in Busemann convex metric spaces date: 2022-10-03 words: 8083 flesch: 83 summary: A is relatively compact, (ii) µ(A) = µ(A) for all A ∈ Σ, (iii) µ(A∪B) = max{µ(A),µ(B)} for all A,B ∈ Σ. xj ∈ X, rj ≤ ε, ∀ 1 ≤ j ≤ n < ∞}, for all A ∈ Σ (see [2] for more details). keywords: convex; pair; point; proximity; spaces; theorem cache: agt-14000.pdf plain text: agt-14000.txt item: #60 of 431 id: agt-14045 author: Roy, Kushal; Panja, Sayantan title: From interpolative contractive mappings to generalized Ciric-quasi contraction mappings date: 2021-04-01 words: 5035 flesch: 83 summary: If a mapping T from a complete metric space (X, d) to itself satisfies the following condition (1.1) d(T x, T y) ≤ αd(x, y) for all x, y ∈ X, for some α ∈ [0, 1) then T possesses a unique fixed point in X. Received 18 July 2020 – Accepted 30 January 2021 http://dx.doi.org/10.4995/agt.2021.14045 K. Roy and S. Panja Several generalizations of this theorem have been made by researchers, work- ing in the area of fixed point theory, by means of different new type contractive mappings. In a metric space (X, d), a mapping T : X → X is said to be interpolative Kannan-type contractive mapping if it satisfies (1.2) d(T x, T y) ≤ keywords: d(t x; t x; t y cache: agt-14045.pdf plain text: agt-14045.txt item: #61 of 431 id: agt-14185 author: Boxer, Laurence title: Convexity and freezing sets in digital topology date: 2021-04-01 words: 7287 flesch: 82 summary: Given a function f : X → X, we say x ∈ X is a fixed point of f if f(x) = x. A set X in a Euclidean space Rn is convex if for every pair of distinct points x, y ∈ X, the line segment xy from x to y is contained in X. keywords: digital; freezing; set cache: agt-14185.pdf plain text: agt-14185.txt item: #62 of 431 id: agt-14332 author: Ahmadi Zand, Mohammad Reza; Khosravi, Zahra title: Remarks on the rings of functions which have a finite numb er of di scontinuities date: 2021-04-01 words: 4443 flesch: 88 summary: Thus, if f ∈ C(X)F and X is T1, then there is a finite closed subset H of X such that f ∈ C(X \ H). It’s obvious that for every x ∈ X, |g(x)h(x)| < π 2 and gh|S = arctan ◦f. keywords: c(x)f; space cache: agt-14332.pdf plain text: agt-14332.txt item: #63 of 431 id: agt-14422 author: Iliadis, S. D.; Sadovnichy, Yu. V. title: On sheaves of Abelian groups and universality date: 2021-04-01 words: 9671 flesch: 87 summary: = U X̄ δ (L), where ε = θA(θ0(η)), δ = θX(η) and L is the element of C(RX), consisting of all elements Xλ ∈ X for which Aλ ∈ H (we shall say that L and H correspond each other). We put A ≡ {Aλ : λ ∈ Λ}, X ≡ {Xλ : λ ∈ Λ}. and consider A and X as indexed by Λ sets of topological spaces. keywords: set cache: agt-14422.pdf plain text: agt-14422.txt item: #64 of 431 id: agt-14446 author: Veisi, Amir; Delbaznasab, Ali title: Metric spaces related to Abelian groups date: 2021-04-01 words: 7067 flesch: 93 summary: For an L-group G and g ∈ G, we let |g| = sup{g, g−1} = g ∨ Let G be a Dedekind-complete densely ordered group, (X, d) a G-metric space, d is bounded, g ∈ G, and let F(X) be the family of all nonempty closed subsets of X. For A, B ∈ F(X) define dB(A) = sup{d(a, B) : a ∈ A}, and d′(A, B) = sup{dA(B), dB(A)}. keywords: d(x; group; metric cache: agt-14446.pdf plain text: agt-14446.txt item: #65 of 431 id: agt-14449 author: Sun, Taixiang; Han, Caihong; Su, Guangwang; Qin, Bin; Li, Lue title: The periodic points of ε-contractive maps in fuzzy metric spaces date: 2021-10-01 words: 4409 flesch: 94 summary: The periodic points of ε-contractive maps in fuzzy metric spaces Taixiang Sun a, Caihong Han a,∗, Guangwang Su a, Bin Qin b and Lue Li a a College of Information and Statistics, Guangxi University of Finance and Economics, Nanning, 530003, China (stx1963@163.com,h198204c@163.com, s1g6w3@163.com, li1982lue@163.com) b Guangxi (ASEAN) Keywords: fuzzy metric space; ε-contractive map; periodic point. keywords: fuzzy cache: agt-14449.pdf plain text: agt-14449.txt item: #66 of 431 id: agt-14542 author: Borat, Ayse title: Digital homotopic distance between digital functions date: 2021-04-01 words: 4247 flesch: 81 summary: After constructing the digital homotopic distance between digital functions, one of our aims is to show the relation between digital homotopic distance and digital Received 27 October 2020 – Accepted 14 December 2020 http://dx.doi.org/10.4995/agt.2021.14542 A. Borat LS category of a digital image as defined in [2] and digital LS cat of a digital function as defined in [18]. 22, no. 1 184 Digital homotopic distance between digital functions Definition 2.6 ([7]). keywords: digital cache: agt-14542.pdf plain text: agt-14542.txt item: #67 of 431 id: agt-14585 author: Sharma, Pranav title: Duality of locally quasi-convex convergence groups date: 2021-04-01 words: 2359 flesch: 75 summary: Keywords: continuous duality; convergence groups; local quasi-convexity; Pontryagin duality. 22, no. 1 194 Duality of locally quasi-convex convergence groups of convergence groups contains the class of topological groups. keywords: convergence; group; quasi cache: agt-14585.pdf plain text: agt-14585.txt item: #68 of 431 id: agt-14589 author: Gopal, Sharan; Imam, Faiz title: Periodic points of solenoidal automorphisms in terms of inverse limits date: 2021-10-01 words: 5453 flesch: 83 summary: Let p ∈ P and np = n (S) p . The dual of a one dimensional solenoid ΣA, where A = (ak) is isomorphic to the subgroup of Q generated by { 1 a1a2···ak : k ∈ N}. keywords: points cache: agt-14589.pdf plain text: agt-14589.txt item: #69 of 431 id: agt-14602 author: Bhattacharjee, Papiya; Knox, Michelle L.; McGovern, Warren Wm. title: Disconnection in the Alexandroff duplicate date: 2021-10-01 words: 6782 flesch: 81 summary: Locally, a point p ∈ X is called a basically disconnected point (or a b.d. point for short) if whenever O and C are disjoint open sets and C is a cozero, then p /∈ clO ∩ clC. A nice source of basically disconnected spaces are P-spaces. This is because if X is compact extremally disconnected and p ∈ X is not isolated, then X r {p} is C∗-embedded in X and thus β(X r {p}) = X and no point of βX r X can be a Gδ-point of βX. keywords: a(x; coz(f; set; space cache: agt-14602.pdf plain text: agt-14602.txt item: #70 of 431 id: agt-14778 author: Singha, Manooranjan; Das, Kousik title: Topological Krasner hyperrings with special emphasis on isomorphism theorems date: 2022-04-01 words: 5696 flesch: 79 summary: For the ease of writing throughout this context, let’s write topological hyperring instead of topological Krasner hyperring. It is investigated that how the difference between hyperoperation and binary operation affects on the theory of topological Krasner hyperring, espe- cially on the topological isomorphisms. keywords: hyperring cache: agt-14778.pdf plain text: agt-14778.txt item: #71 of 431 id: agt-14809 author: Singh, Beenu; Singh, Davinder title: Sum connectedness in proximity spaces date: 2021-10-01 words: 5110 flesch: 83 summary: � Now, we find the relation of sum δ-connectedness of proximity space with its Stone-Čech compactification. Let U be a δ-open δ-quasi component of proximity space X and x ∈ U. Let V be the δ-component of x. keywords: proximity; space; sum; sum δ cache: agt-14809.pdf plain text: agt-14809.txt item: #72 of 431 id: agt-14846 author: Iqbal, Muhammad Asad; Khan, Moiz ud Din title: Selection principles: s-Menger and s-Rothberger-bounded groups date: 2022-04-01 words: 5169 flesch: 87 summary: An ITG (G,∗,τ) is: (1) s-Menger-bounded if for each sequence (Pn)n∈N of semi-open nbds of the neutral element e ∈ G, there exists a sequence (Qn)n∈N of finite subsets of G such that G = ⋃ n∈N Qn ∗Pn. (2) s-Rothberger-bounded if for each sequence (Pn)n∈N of semi-open nbds of the neutral element e ∈ G, there exists a sequence (pn)n∈N of ele- ments of G such that G = ⋃ n∈N pn ∗Pn. (3) s-Hurewicz-bounded if there is for each sequence (Pn)n∈N of semi open nbdss of neutral element e ∈ G, there exists a sequence (Qn)n∈N of finite subsets of G such that each x ∈G belongs to all but finitely many Qn ∗Pn. Let (G,∗) be a subgroup of group (H,∗). Then obviously G ∩ m ∗ Rn 6= φ, and so pm ∈ G is belonging to G∩m∗Rn. keywords: groups; semi cache: agt-14846.pdf plain text: agt-14846.txt item: #73 of 431 id: agt-14868 author: Sharmah, Ankur; Hazarika, Debajit title: Further aspects of I K-convergence in topological spaces date: 2021-10-01 words: 5414 flesch: 85 summary: Now, Let K = N∁ ∈ K, I = M∁ Therefore, there exists K ∈ K such that {s ∈ S : f(s) /∈ keywords: convergence; space cache: agt-14868.pdf plain text: agt-14868.txt item: #74 of 431 id: agt-14915 author: Bayih, Tilahun; Dube, Themba; Ighedo, Oghenetega title: On the Menger and almost Menger properties in locales date: 2021-04-01 words: 11066 flesch: 81 summary: In Section 2 we study some properties of Menger frames. � Since every Menger frame is Lindelöf and every subframe of a Menger frame is Menger, we deduce the following characterisation of Menger frames from this proposition. keywords: cover; frame; menger; open; sequence; ∈ n cache: agt-14915.pdf plain text: agt-14915.txt item: #75 of 431 id: agt-15061 author: Dahia, Elhadj; Hamidi, Khaled title: Lipschitz integral operators represented by vector measures date: 2021-10-01 words: 6851 flesch: 79 summary: Lipschitz Pietsch-∞-integral operators In this section we extend the definition of the class of Pietsch-∞-integral lin- ear operators to the case of Lipschitz operators and we will show a factorization theorem that characterizes these mappings. Furthermore, if (A,‖·‖A) is a Banach operator ideal then (A◦Lip0,‖·‖A◦Lip0) is Banach Lipschitz operator ideal with ‖T‖A◦Lip0 = ‖TL‖A . keywords: banach; lipschitz; measure; operators; pietsch; space cache: agt-15061.pdf plain text: agt-15061.txt item: #76 of 431 id: agt-15101 author: Kholturayev, Kholsaid Fayzullayevich title: Geometrical properties of the space of idempotent probability measures date: 2021-10-01 words: 7379 flesch: 79 summary: X −→ Z, g(a) = g(b) = a, g(c) = c. Consider compact Hausdorff spaces X, Y × Z, and the map (f, g): X −→ Y × Z. Let I(X) denote the set of all idempotent probability measures on a com- pact Hausdorff space X, and RC(X) be a set of all maps C(X) → R. Obviously I(X) ⊂ RC(X). keywords: c(x; compact; i(x; i=1; probability; space cache: agt-15101.pdf plain text: agt-15101.txt item: #77 of 431 id: agt-15187 author: Burke, John; Pinheiro, Leonardo title: Topologically mixing extensions of endomorphisms on Polish groups date: 2022-04-01 words: 3193 flesch: 75 summary: Consider a bounded metric d on G, we can define a metric ρ on ∏∞ i=1 G by ρ(g,h) = ∞∑ i=1 d(gi,hi) 2i , forf,g ∈ G which induces the product topology on ∏∞ i=1 G. For each g ∈ ∏∞ i=1 G , write g = (g1,g2,g3, · · ·), gi ∈ G, and define the maps Φ, Ψ : ∏∞ i=1 G → ∏∞ i=1 G by Φ(g) = (ϕ(g1)g2,g3,g4, · · ·) and Ψ(g) = (e,g1,g2,g3, · · ·) where e is the identity in G. keywords: group; mixing cache: agt-15187.pdf plain text: agt-15187.txt item: #78 of 431 id: agt-15214 author: Aslantaş, Mustafa; Sahin, Hakan; Sadullah, Uğur title: Some generalizations for mixed multivalued mappings date: 2022-04-01 words: 3380 flesch: 86 summary: For some examples of partial metric space, we refer to [1, 5, 8, 21]. [5] I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. keywords: metric cache: agt-15214.pdf plain text: agt-15214.txt item: #79 of 431 id: agt-15231 author: Sereti, Fotini title: Small and large inductive dimension for ideal topological spaces date: 2021-10-01 words: 8506 flesch: 86 summary: How- ever, researches for dimensions in the field of ideal topological spaces are in an initial stage. The main notion of ideal topological space was studied in Kuratowski’s monograph keywords: ideal; ind(x cache: agt-15231.pdf plain text: agt-15231.txt item: #80 of 431 id: agt-15356 author: Bera, Ashis; Dey, Lakshmi Kanta; Som, Sumit; Garai, Hiranmoy; Sintunavarat, Wutiphol title: Boyd-Wong contractions in F-metric spaces and applications date: 2022-04-01 words: 4400 flesch: 83 summary: Introduction and Preliminaries After the invention of metric spaces by Frèchet, many mathematicians have generalized the metric structure by making some changes in the original def- inition of a metric given by Frèchet. [15] M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl. keywords: metric; point cache: agt-15356.pdf plain text: agt-15356.txt item: #81 of 431 id: agt-15561 author: Bisht, Ravindra K.; Rakocević, Vladimir title: On a probabilistic version of Meir-Keeler type fixed point theorem for a family of discontinuous operators date: 2021-10-01 words: 5318 flesch: 81 summary: Keywords: Menger PM-spaces; fixed point; almost orbital continuity; non- expansive mapping. Fixed points of a family of Meir-Keeler type mappings in Menger PM-space. keywords: fixed; point cache: agt-15561.pdf plain text: agt-15561.txt item: #82 of 431 id: agt-15566 author: Beshimov, R. B.; Georgiou, Dimitrios N.; Zhuraev, R. M. title: Index boundedness and uniform connectedness of space of the G-permutation degree date: 2021-10-01 words: 5915 flesch: 91 summary: For an entourage U ∈ U and a point x ∈ T the set U(x) = {y ∈ T : (x, y) ∈ U} is called the U-ball centered at x. For a subset A ⊂ T the set U(A) = ⋃ a∈A U(a) is called the U-neighborhood of A U ∈ U}. keywords: space cache: agt-15566.pdf plain text: agt-15566.txt item: #83 of 431 id: agt-15571 author: Afshari, Hojjat; Shojaat, Hadi; Fulga, Andreea title: Common new fixed point results on b-cone Banach spaces over Banach algebras date: 2022-04-01 words: 5302 flesch: 92 summary: P ⊂ E a cone and θ be the zero of E, also there is a partial ordering ≤ such that ξ ≤ ζ iff ζ − ξ ∈ P. Write ξ � ζ for ζ − ξ ∈ intP, where intP is the interior set of P. [19] E. Karapinar, Fixed point theorems in cone Banach spaces, Fixed Point Theory Appl. 2009, Art. ID 609281. keywords: cone; k′1; ξ2n cache: agt-15571.pdf plain text: agt-15571.txt item: #84 of 431 id: agt-15586 author: Szymanski, Andrzej A title: Alexandroff duplicate and βκ date: 2022-04-01 words: 5040 flesch: 80 summary: It means that (4) For each non-isolated point p ∈ X, the family {U −F : U is an open neighborhood of p and F is a finite subset of X} is a base for the ultrafilter p. Finally, considering A (X) as a subspace of β (X′), one can also observe the following phenomenon: Let p ∈ X be a non-isolated point of X. keywords: space cache: agt-15586.pdf plain text: agt-15586.txt item: #85 of 431 id: agt-15610 author: Jäger, Gunther; Ahsanullah, T. M. G. title: Quantale-valued Cauchy tower spaces and completeness date: 2021-10-01 words: 11937 flesch: 93 summary: Then there are F ∈ F such that for all x, y ∈ F we have d(x, y) ≥ α′ and G ∈ G such that for all u, v ∈ G we have d(u, v) ≥ β′. Then there is F ∈ F such that for all x, y ∈ F there is β ≥ ǫ with [x] ∧ keywords: d(x; f ∈; space; tower cache: agt-15610.pdf plain text: agt-15610.txt item: #86 of 431 id: agt-15613 author: Mandal, Pabitra Narayan title: Topological transitivity of the normalized maps induced by linear operators date: 2022-04-01 words: 4476 flesch: 78 summary: Let T ∈ L(X). Let T ∈ L(X). keywords: cone; transitivity cache: agt-15613.pdf plain text: agt-15613.txt item: #87 of 431 id: agt-15668 author: Golrizkhatami, F.; Taherifar, Ali title: Some classes of topological spaces related to zero-sets date: 2022-04-01 words: 8016 flesch: 90 summary: � A point p ∈ X is said to be an almost P-point if f ∈ Mp, intX Z(f) 6= ∅, and X is called an almost P-space if every point of X is an almost P-point. Then p ∈ X and there is an open subset U of T such that p ∈ U ∩ X ⊆ Z(ft). keywords: c(x; cap; i∈n; set; space cache: agt-15668.pdf plain text: agt-15668.txt item: #88 of 431 id: agt-15669 author: Tri, Vo Viet title: Fixed point index computations for multivalued mapping and application to the problem of positive eigenvalues in ordered space date: 2022-04-01 words: 5389 flesch: 82 summary: For any x ∈ S with x = u + y,y ∈ K, we have 〈p0,x〉 = 〈p0,u〉 + 〈p0,y〉≥ µ0. Indeed, if there exists y ∈ K such that 〈p1,y〉 < 0, using (3.17) for x = u + ny, (n = 1, 2, ...) keywords: fixed; point cache: agt-15669.pdf plain text: agt-15669.txt item: #89 of 431 id: agt-15739 author: Olela Otafudu, Olivier; Sebogodi, Katlego title: On w-Isbell-convexity date: 2022-04-01 words: 6226 flesch: 84 summary: Chistyakov equipped Xw with the metric qw, where qw(x,y) = inf{λ > 0 : w(λ,x,y) ≤ λ} whenever x,y ∈ Xw. whenever x,y ∈ Xw is a (pseudo) metric on Xw whenever w is modular (pseudo) metric on X. keywords: modular cache: agt-15739.pdf plain text: agt-15739.txt item: #90 of 431 id: agt-15745 author: Martínez, Luis; Tapia, Héctor Pinedo; Ramirez, Edwar title: Partial actions of groups on hyperspaces date: 2022-10-03 words: 6885 flesch: 87 summary: Introduction Given an action µ : G×Y → Y of a group G on a set Y and an invariant subset X of Y (i.e., µ(g,x) ∈ X, for all x ∈ X, and g ∈ G), the restriction of µ to G×X determines an action of G on X. This is a collection of partially defined maps θg (g ∈ G) on X satisfying θ1 = idX and θgh is an extension of the composition θg◦θh, for all g,h ∈ G. keywords: action cache: agt-15745.pdf plain text: agt-15745.txt item: #91 of 431 id: agt-1575 author: Tarizadeh, Abolfazl title: On the category of profinite spaces as a reflective subcategory date: 2013-07-02 words: 5449 flesch: 80 summary: + rnen where r,ri ∈ R and ei ∈ M, if we multiply this equation to 1 − x then we get 1 − x But for each element e of a set of idempotent generators of N, we have e = en ∈ M for some n ≥ 1. keywords: space cache: agt-1575.pdf plain text: agt-1575.txt item: #92 of 431 id: agt-1583 author: Mukherjee, M. N.; Mandal, Dhananjoy title: Concerning nearly metrizable spaces date: 2013-07-21 words: 5305 flesch: 80 summary: Thus A is a local pseudo-base at x in X. � The following is a well known characterization for metrizable spaces, which may be found in page 192 of [9]. � Another nice characterization of metrizable spaces can be found in [9]. keywords: space cache: agt-1583.pdf plain text: agt-1583.txt item: #93 of 431 id: agt-15844 author: Veisi, Amir title: Closed ideals in the functionally countable subalgebra of C(X) date: 2022-04-01 words: 6438 flesch: 90 summary: If X is zero-dimensional and f,g ∈ Cc(X), then clβ0XZ(f) is a neighborhood of clβ0XZ(g) if and only if there exists h ∈ Cc(X) such that Z(g) ⊆ coz(h) ⊆ Z(f). f ∈ Cc(X)} is called a zc-filter if it is a filter on X. keywords: cc(x; ideal cache: agt-15844.pdf plain text: agt-15844.txt item: #94 of 431 id: agt-1586 author: Yousefian Darani, Ahmad; Motmaen, Shahram title: Zariski topology on the spectrum of graded classical prime submodules date: 2013-07-21 words: 5801 flesch: 84 summary: In section 3 we introduce and study the concept of graded classical prime submodules and define the quasi-Zariski topology on the spectrum of all graded classical prime submodules of a graded module. 14, no. 2 160 Zariski topology on the spectrum of graded classical prime submodules all g, h ∈ G, RgRh ⊆ Rgh. keywords: prime; submodule cache: agt-1586.pdf plain text: agt-1586.txt item: #95 of 431 id: agt-1587 author: Protasov, Igor V. title: The combinatorial derivation date: 2013-09-18 words: 3565 flesch: 85 summary: = {g ∈ G : |gA ∩ A| = ∞}. For each g ∈ G, we have µ(gAi ∩ gkAi) > 0 keywords: group; subset; ∆(a cache: agt-1587.pdf plain text: agt-1587.txt item: #96 of 431 id: agt-1588 author: Bayhan, Sadik; Kanibir, A.; Reilly, Ivan L. title: On functions between generalized topological spaces date: 2013-07-25 words: 4031 flesch: 66 summary: On functions between generalized topological spaces Let gX and gY be generalized topologies on X and Y, respectively. In the past decade, Császár [4] and others have been considering generalized topological spaces, and developing a theory for them. keywords: open cache: agt-1588.pdf plain text: agt-1588.txt item: #97 of 431 id: agt-15893 author: Boxer, Laurence title: Beyond the Hausdorff metric in digital topology date: 2022-04-01 words: 3638 flesch: 80 summary: By hypothesis, given x ∈ A and y ∈ B, there exist x′ ∈ A, y′ ∈ B, and cu-paths P from x to y ′ and Q from y to x′ in X such that each of P and Q has length of at most m. Since each cu-adjacency corresponds to a Euclidean distance of at most u1/p, it follows that dp(x,y ′) Then there exists y ∈ B keywords: digital; metric cache: agt-15893.pdf plain text: agt-15893.txt item: #98 of 431 id: agt-15963 author: Boureni, Dalila; Georgiev, Svetlin; Kheloufi, Arezki; Mebarki, Karima title: Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach date: 2022-10-03 words: 6097 flesch: 87 summary: t ∈ and we find ρ(0,x) = ρ0(x), x ∈ R. Now, we differentiate the second equation of (2.6) with respect to t and x and we find (ρu)t(t,x) keywords: equations cache: agt-15963.pdf plain text: agt-15963.txt item: #99 of 431 id: agt-1608 author: Kohli, J.K.; Arya, C.P. title: Upper and lower cl-supercontinuous multifunctions date: 2013-07-23 words: 8144 flesch: 78 summary: A point x ∈ X is said to be a cl-adherent point of A if every clopen set containing x intersects A. Let X ⊸ Y is called a multifunction from X into Y if for each x ∈ X, ϕ(x) is a nonempty subset of Upper and lower cl-supercontinuous multifunctions 3 Y. Let B be a subset of Y. Then the set ϕ−1+ (B) = {x ∈ X : ϕ(x) ∩ B 6= ∅} is called large inverse image[6]1 of B and the set ϕ−1− (B) = {x ∈ X : ϕ(x) ⊂ B} is called small inverse image of B. The set Γϕ = {(x,y) ∈ X × keywords: open; set; supercontinuous; upper cache: agt-1608.pdf plain text: agt-1608.txt item: #100 of 431 id: agt-16126 author: Pal, Sudip Kumar; Chakraborty, Sagar title: On certain new notion of order Cauchy sequences, continuity in (l)-group date: 2022-04-01 words: 6663 flesch: 76 summary: Some author use the term monotone sequences instead of order sequence. Let (xn) be an order quasi-Cauchy sequence of points on E. As (fn) is uniformly order convergent to f, given order sequence (pn) in L such that for each n0 ∈ N, there exists some m keywords: cauchy; order; order sequence; quasi; sequence; ward cache: agt-16126.pdf plain text: agt-16126.txt item: #101 of 431 id: agt-16128 author: Pataki, Gergely title: Investigation of topological spaces using relators date: 2022-04-01 words: 4064 flesch: 76 summary: For the converse inclusion let R ∈ R, x ∈ X and A = intR(R(x)). With the usual notations, the statement R is a relator on X means that X 6= ∅, ∅ 6= R⊂ Exp(X2), where Exp(X) is the power set of X, and X2 = X ×X. If R is a relation on X, x ∈ X, and A ⊂ X, then the sets R(x) = {y ∈ X : (x,y) ∈ R}, and R[A] keywords: relator cache: agt-16128.pdf plain text: agt-16128.txt item: #102 of 431 id: agt-1613 author: Acosta, Lorenzo; Rubio, I. Marcela title: On star compactifications date: 2013-07-25 words: 6990 flesch: 76 summary: 17-32 On star compactifications Lorenzo Acosta and I. Marcela Rubio Abstract We study the ordered structure of the collection of star compactifica- tions by n points and the behavior of these compactifications through quotients obtained by identification of additional points. These examples of compactifications by a finite number of points are parti- cular cases of star compactifications. keywords: compactification cache: agt-1613.pdf plain text: agt-1613.txt item: #103 of 431 id: agt-1614 author: Comfort, W. W.; Hager, A. W. title: Range-preserving AE(0)-spaces date: 2013-07-25 words: 3312 flesch: 82 summary: S ∈ AE(0)rp; and (c) S ⊆ T , S compact ⇒ S ∈ AE(0)rp. This shows T ∈ AE(0)rp. keywords: ae(0)rp; space cache: agt-1614.pdf plain text: agt-1614.txt item: #104 of 431 id: agt-16143 author: Ali Akbar, Kamaludheen; Mubeena, T. title: On the group of homeomorphisms on R: A revisit date: 2022-10-03 words: 5952 flesch: 89 summary: Suppose there exists f ∈ N with adjacent fixed points t1 < t2. This proves H ⊂ N whenever there exists f ∈ N with adjacent fixed points. keywords: group; ih(r cache: agt-16143.pdf plain text: agt-16143.txt item: #105 of 431 id: agt-1616 author: Banaschewski, B.; Hager, A. W. title: Epimorphisms and maximal covers in categories of compact spaces date: 2013-04-01 words: 4927 flesch: 80 summary: � We say (R, r) is epireflective in C if R is a subcategory of C, and for each Y ∈ C there is rY ∈ R (the reflection) and epi rY Y rY oo (the reflection map) for which, whenever X Y f oo with X ∈ R, there is f̄ with f̄rY = f. (See [11] for a full account of the theory of epireflective subcategories). The next largest is R({0, 1}): if R is epireflective and not R({0}), there is X ∈ R with |X| ≥ 2, thus {0, 1} ∈ R, so R({0, 1}) keywords: cover; epi cache: agt-1616.pdf plain text: agt-1616.txt item: #106 of 431 id: agt-16165 author: Shukla, Rahul; Pant, Rajendra title: Some fixed point results for enriched nonexpansive type mappings in Banach spaces date: 2022-04-01 words: 5200 flesch: 83 summary: Keywords: nonexpansive mapping; enriched nonexpansive mapping; Ba- nach space. References [1] V. Berinde, Approximating fixed points of enriched nonexpansive mappings by Kras- noselskij iteration in Hilbert spaces, Carpathian J. Math. 35 (2019), 293–304. keywords: f(ξ; mapping cache: agt-16165.pdf plain text: agt-16165.txt item: #107 of 431 id: agt-1618 author: Capraro, Valerio title: A notion of continuity in discrete spaces and applications date: 2013-04-01 words: 4716 flesch: 76 summary: We use this notion of continuity to derive an analogue in Z2 of the Jordan curve theorem and to extend to a quite large class of locally finite metric spaces (containing all finite metric spaces) an inequality for the ℓp-distortion of a metric space that has been recently proved by Pierre-Nicolas Jolissaint and Alain Valette for finite connected graphs. This inequality was recently proved for finite connected graphs by Pierre- Nicolas Jolissaint and Alain Valette (see [9], Theorem 1). keywords: finite; metric; path cache: agt-1618.pdf plain text: agt-1618.txt item: #108 of 431 id: agt-1619 author: Esty, Norah title: The hyperspaces Cn(X) for finite ray-graphs date: 2013-04-01 words: 4881 flesch: 81 summary: If X ∈ X is a k-legged graph, then for all n, the hyperspace (Cn(X), τH) has at least 2 k connected components. Proof. Let X ∈ X be a graph with k distinct rays, labelled R1, . . . keywords: c(x; cn(x; topology cache: agt-1619.pdf plain text: agt-1619.txt item: #109 of 431 id: agt-1620 author: Qahis, Abdo; Noorani, Mohd. Salmi Md. title: Strongly path-confluent mappings date: 2013-04-01 words: 4740 flesch: 79 summary: The composition properties We say that a class M of mappings has the composition property provided that for any two mappings f : X −→ Y and g : Y −→ Z belonging to M then their composition gof belongs to M. Also, we say that a class M of map- pings has the composition factor property provided that for any two mappings f : X −→ Y and g : Y −→ Z such that gof belongs to M, then g belongs to M. � The following proposition shows that if the mapping f : X −→ Y has the component restriction property, then it also has the path-component restriction property, which means that the path-component restriction property is weaker notion than the notion of component restriction property. keywords: confluent; mapping; path cache: agt-1620.pdf plain text: agt-1620.txt item: #110 of 431 id: agt-1621 author: Dridi, Lobna; Lazaar, Sami; Turki, Tarek title: F-door spaces and F-submaximal spaces date: 2013-04-01 words: 7466 flesch: 84 summary: Alexandroff Topology According to Kennisson, a flow in a category C is a couple (X, f), where X is an object of C and f : X −→ X is a morphism, called the iterator (see [25] and [26]). (A topological space X is said to be maximal if and only if for any point x ∈ X, {x} is not open). keywords: door; space; submaximal; subset cache: agt-1621.pdf plain text: agt-1621.txt item: #111 of 431 id: agt-1622 author: Kohli, J.K.; Singh, D.; Aggarwal, Jeetendra; Rana, Manoj title: Pseudo perfectly continuous functions and closedness/compactness of their function spaces date: 2013-04-01 words: 8804 flesch: 72 summary: However, Naimpally [46] showed that in contrast to continuous functions the set S(X, Y ) of strongly continuous functions is closed in Y X in the topology 116 J. K. Kohli, D. Singh, J. Aggarwal and M. Rana of pointwise convergence if X is locally connected and Y is Hausdorff. Naimpally’s result [46] that in contrast to continuous functions, the set S(X, Y ) of strongly continuous functions is closed in Y X in the topology of pointwise convergence if X is locally connected and Y is Hausdorff; is extended to a larger framework by Kohli and Singh keywords: function; open; pseudo; set; space; topology cache: agt-1622.pdf plain text: agt-1622.txt item: #112 of 431 id: agt-1623 author: Davis, Simon title: Supersymmetry and the Hopf fibration date: 2012-10-01 words: 3967 flesch: 74 summary: 2010 MSC: 14D21, 55F20, 81Q60 Keywords: spectral sequence, Hopf fibration, supersymmetry 1. The BRST cohomology of quantum field theories has been calculated previ- ously with spectral sequences [19]. keywords: fibration cache: agt-1623.pdf plain text: agt-1623.txt item: #113 of 431 id: agt-1624 author: Li, Ji; Peters, T. J.; Marsh, D.; Jordan, K. E. title: Computational Topology Counterexamples with 3D Visualization of Bézier Curves date: 2012-10-01 words: 5933 flesch: 63 summary: Unknotted Bézier curves with equilateral control polygons 3.1. 115-134 Computational Topology Counterexamples with 3D Visualization of Bézier Curves J. Li, T. J. Peters∗, D. Marsh and K. E. Jordan Abstract For applications in computing, Bézier curves are pervasive and are defined by a piecewise linear curve L which is embedded in R 3 and yields a smooth polynomial curve C embedded in R 3 . keywords: bézier; control; curve; figure; knot; polygon; self cache: agt-1624.pdf plain text: agt-1624.txt item: #114 of 431 id: agt-1625 author: Morales López, Luis Felipe title: Continuous isomorphisms onto separable groups date: 2012-10-01 words: 8744 flesch: 84 summary: g ∈ G \ {e}, o(g) = ∞; • a torsion group if for every element g ∈ G, o(g) < ∞; • bounded torsion if there exists n ∈ N such that gn = e for every g ∈ G; • unbounded torsion if G is torsion and for each n ∈ N there exists g ∈ G such that o(g) > n; • a divisible group if for every g ∈ G and n ∈ N, there is h ∈ G such that hn = g; • a p-group, for a prime p, if the order of any element of G is a power of p. keywords: continuous; group; separable cache: agt-1625.pdf plain text: agt-1625.txt item: #115 of 431 id: agt-1626 author: Nashine, Hemant Kumar; Aydi, Hassen title: Common fixed points for generalized (v,o)-weak contractions in ordered cone metric spaces date: 2012-10-01 words: 6137 flesch: 87 summary: Common fixed points in ordered cone metric spaces 153 Definition 2.2. Common fixed points for generalized (,)-weak contractions in ordered cone metric spaces. keywords: cone; metric; point; spaces cache: agt-1626.pdf plain text: agt-1626.txt item: #116 of 431 id: agt-1627 author: Karlova, Olena title: Classification of separately continuous mappings with values in o-metrizable spaces date: 2012-10-01 words: 6165 flesch: 84 summary: : Y ×Y ×[0, 1] → Y such that λ(y, z, 0) = y and λ(y, z, 1) = z for all y, z ∈ Y . [0, 1] → X is defined by the formula λ(x, y, t) = (1 − t)x + ty, x, y ∈ X, keywords: space cache: agt-1627.pdf plain text: agt-1627.txt item: #117 of 431 id: agt-1628 author: Altun, Ishak; Durmaz, Gonca title: Weak partial metric spaces and some fixed point results date: 2012-10-01 words: 4481 flesch: 92 summary: If x > y > 0, then p(Fx, Fy) = p(x − 1, y − 1) = x + y − 2 2 ≤ 9 10 x + y 2 = 9 10 p(x, y). Also, Heckmann shows that, if p is a weak partial metric on X, then for all x, y ∈ X, we have the following weak small self-distance property p(x, y) ≥ p(x, x) + p(y, y) 2 . keywords: p(x cache: agt-1628.pdf plain text: agt-1628.txt item: #118 of 431 id: agt-1629 author: Aydi, Hassen; Abbas, Mujahid title: Tripled coincidence and fixed point results in partial metric spaces date: 2012-10-01 words: 5904 flesch: 88 summary: An element (x, y, z) ∈ X3 is called a tripled fixed point of a given mapping F : X3 → X if x = F(x, y, z), y = F(y, z, x) and z = F(z, x, y). 193-206 Tripled coincidence and fixed point results in partial metric spaces Hassen Aydi and Mujahid Abbas Abstract In this paper, we introduce the concept of W -compatiblity of mappings F : X × X × X → X and g : X → X and based on this notion, we obtain tripled coincidence and common tripled fixed point results in the setting of partial metric spaces. keywords: metric; point cache: agt-1629.pdf plain text: agt-1629.txt item: #119 of 431 id: agt-1630 author: Minguzzi, E. title: Compactification of closed preordered spaces date: 2012-10-01 words: 8450 flesch: 69 summary: Abstract A topological preordered space admits a Hausdorff T2-preorder com- pactification if and only if it is Tychonoff and the preorder is represented by the family of continuous isotone functions. We shall mostly work with continuous isotone functions with value in [0,1], although we could equivalently work with bounded continuous isotone functions. keywords: compactification; isotone; preorder; space cache: agt-1630.pdf plain text: agt-1630.txt item: #120 of 431 id: agt-1632 author: Khosravi, Behnam title: On cofree S-spaces and cofree S-flows date: 2012-04-15 words: 4488 flesch: 79 summary: Keywords: S-space, S-flow, Cofree S-space, Cofree S-flow Compact-open topology, Injective S-space. → S × X, t(s,x) = (ts,x), is denoted by L(X). keywords: cco(s; cofree; space cache: agt-1632.pdf plain text: agt-1632.txt item: #121 of 431 id: agt-1633 author: Alas, Ofelia T.; Madriz-Mendoza, Maira; Wilson, Richard G. title: Some results and examples concerning Whyburn spaces date: 2012-04-15 words: 4092 flesch: 80 summary: 12 O. T. Alas, M. Madriz-Mendoza and R. G. Wilson 2. Whyburn and weakly Whyburn spaces The sufficiency is clear, since K∩A is not closed in K. For the necessity, suppose that (X,τ) is a Hausdorff weakly Whyburn k-space and that A ⊆ X is not closed in X. keywords: space; whyburn cache: agt-1633.pdf plain text: agt-1633.txt item: #122 of 431 id: agt-16332 author: Salam, Saif; Al-Zoubi, Khaldoun title: The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring date: 2022-10-03 words: 9273 flesch: 93 summary: A proper graded submodule P of M is called a graded prime submodule of M if whenever r ∈ h(R) and m ∈ h(M) with rm ∈ P , then either m ∈ P or r ∈ (P :R M). The graded prime spectrum of M, denoted by SpecG(M), is the set of all graded prime submodules of M. A proper graded submodule Q of M is called a graded primary submodule of M, if whenever r ∈ h(R) and m ∈ h(M) with rm ∈ Q, then either m ∈ Q or r ∈ Gr((Q :R M)). keywords: grm; module; psg(m; r m cache: agt-16332.pdf plain text: agt-16332.txt item: #123 of 431 id: agt-1636 author: Iurato, Giuseppe title: On density and π-weight of Lp(βN,R, μ) date: 2012-04-15 words: 2679 flesch: 71 summary: There exist however separable spaces that are not selectively separable, as, for example, the Tychonov cube Ic of weight c 3There exists a fourth way, based on integration theory over separable measure spaces (see [5], and [16], Chap. keywords: space cache: agt-1636.pdf plain text: agt-1636.txt item: #124 of 431 id: agt-1637 author: Abohalfya, F.; Raphael, R. title: Aspects of RG-spaces date: 2012-04-15 words: 5513 flesch: 84 summary: 2010 MSC: Primary 54G10; Secondary 46E25, 16E50 Keywords: almost Baire spaces, RG-spaces, Blumberg spaces, almost re- solvable spaces, spaces of countable pseudocharacter, prime z- ideal, P-space, almost-P space 1. Spaces of countable pseudocharacter and Blumberg spaces Definition 5.1. keywords: baire; space; subset cache: agt-1637.pdf plain text: agt-1637.txt item: #125 of 431 id: agt-1638 author: Daniel, D.; Tuncali, M. title: Hereditary separability in Hausdorff continua date: 2012-04-15 words: 4884 flesch: 72 summary: Separable continua may arise in locally connected Suslinian continua in a somewhat natural way by utilizing related equivalence relations. [3] D. E. Cameron, On subspaces of separable spaces, Math. keywords: continuum; hereditarily; rim; separable cache: agt-1638.pdf plain text: agt-1638.txt item: #126 of 431 id: agt-1639 author: Günther, Bernd title: Random selection of Borel sets II date: 2012-04-15 words: 7894 flesch: 84 summary: − fn(1 − t) = 2t − 1 for all n, thus gn(t) := t − fn(t) is symmetric around 12, gn(1 − t) = gn(t), g0(t) = t(1 − t), gn+1(t) ∣∣∣x00 = t + u min (t,1 − t)) keywords: borel; random; sets; xnm cache: agt-1639.pdf plain text: agt-1639.txt item: #127 of 431 id: agt-1640 author: Minguzzi, E. title: Topological conditions for the representation of preorders by continuous utilities date: 2012-04-15 words: 4381 flesch: 67 summary: A topological preordered space E is convex if for every x ∈ E, and open set O x, there are an open decreasing set U and an open increasing set V such that x ∈ U ∩ V ⊂ O. Notice that according to this terminology the statement “the topological preordered space E is convex” differs from the statement “the subset E is convex” (which is always true). 82 E. Minguzzi To start with, it will be convenient to recall some notions from the theory of topological preordered spaces keywords: closed; compact; set; space cache: agt-1640.pdf plain text: agt-1640.txt item: #128 of 431 id: agt-16405 author: Pajoohesh, Homeira title: Representations of bornologies date: 2022-04-01 words: 7713 flesch: 89 summary: The structure (M, +, 0,≤) is an (abelian) po-monoid if M 6= {0} and (M, +, 0) is an (abelian) monoid which is equipped with a partial order ≤ such that for every a,x,y ∈ M, x ≤ y implies a+x ≤ a+y and x+a ≤ y+a. = { (0, 0), if x ∈ K (0, 1), if x 6∈ K . keywords: set cache: agt-16405.pdf plain text: agt-16405.txt item: #129 of 431 id: agt-1641 author: Megaritis, A.C. title: Relative dimension r-dim and finite spaces date: 2012-04-15 words: 4170 flesch: 93 summary: Finite spaces and dimension r-dim In this section we present some propositions concerning the dimension r-dim of a pair (Q, X), where Q is a subset of a finite space X. Proposition 2.1. , xn} is a finite space with n elements, Q ⊆ X, T = (tij), i = 1, . . keywords: finite cache: agt-1641.pdf plain text: agt-1641.txt item: #130 of 431 id: agt-1644 author: Caterino, Alessandro; Vipera, M. Cristina title: Extensions defined using bornologies date: 2013-07-31 words: 7107 flesch: 85 summary: (i) We only have to prove that if for y ∈ Y , y /∈ If z ∈ Y \ W then z /∈ keywords: extension; open cache: agt-1644.pdf plain text: agt-1644.txt item: #131 of 431 id: agt-1645 author: Wang, Huoyung; Fu, Heman title: Some remarks on chaos in topological dynamics date: 2011-10-01 words: 2819 flesch: 83 summary: A TDS (X, f) is (topologically) weakly mixing if (X × X, f × f) is (topologically) transitive. = 0} is a dense Gδ set of X × X because (X, f) is chaotic. keywords: tds cache: agt-1645.pdf plain text: agt-1645.txt item: #132 of 431 id: agt-1646 author: Frascella, Anna; Guido, Cosimo; Solovyov, Sergey A. title: Dual attachment pairs in categorically-algebraic topology date: 2011-10-01 words: 15846 flesch: 68 summary: [8] C. L. Chang, Fuzzy topological spaces, J. Math. Based in category theory and universal algebra, the new framework is called categorically-algebraic (catalg) topology keywords: algebraic; attachment; category; definition; dual; functor; fuzzy; lattice; proposition; set; theory; topology; variety; −−−→ cache: agt-1646.pdf plain text: agt-1646.txt item: #133 of 431 id: agt-1647 author: Fawakhreh, Anwar Jabor; Kiliçman, Adem title: Mappings on weakly Lindelöf and weakly regular-Lindel¨of spaces date: 2011-10-01 words: 2777 flesch: 78 summary: 135-141 Mappings on weakly Lindelöf and weakly regular-Lindelöf spaces Anwar Jabor Fawakhreh and Adem Kılıçman Abstract In this paper we study the effect of mappings and some decompositions of continuity on weakly Lindelöf spaces and weakly regular-Lindelöf spaces. For weakly Lindelöf spaces we give the following theorem. keywords: lindelöf; regular cache: agt-1647.pdf plain text: agt-1647.txt item: #134 of 431 id: agt-1648 author: Jordan, Francisco; Mynard, Frédéric title: Core compactness and diagonality in spaces of open sets date: 2011-10-01 words: 10564 flesch: 79 summary: Let x ∈ X and U ∈ O(x). Then there is x ∈ X, U ∈ O(x) and a family H of filters on X with an injective map θ : H → O(U) such that θ(H) ∩ adhX H = ∅ for each H ∈ H but x ∈ adhX ∧ H∈H H. Define a relation ∼ on H by H1 ∼ H2 provided that 156 F. Jordan and F. Mynard the collections {cl(H): H ∈ H1} and {cl(H): H ∈ H2} both generate the same filter. keywords: compact; convergence; core; open; space; topology cache: agt-1648.pdf plain text: agt-1648.txt item: #135 of 431 id: agt-1650 author: Milani, Vida; Rezaei, Ali Asghar; Mansourbeigi, Seyed M.H. title: Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds date: 2011-10-01 words: 4182 flesch: 73 summary: The dual concept of CW complexes , with some regards, is the notion of noncommutative CW complexes ([7] and [15]). I = {f ∈ A : f(T 2) = 0} ≃ 0, WI = {J ∈ Prim(A) : keywords: complex; let; morse; noncommutative; prim(a cache: agt-1650.pdf plain text: agt-1650.txt item: #136 of 431 id: agt-1652 author: Georgiou, D. N.; Iliadis, Stavros; Megaritis, A. C. title: Universal elements for some classes of spaces date: 2011-10-01 words: 9728 flesch: 85 summary: For dimension-like function Dm IK,IB IE,ν this follows immediately by the fact that X ∈ IE and the class IE is IB-hereditary-separated. For dimension-like function w-Dm IK,IB IE,ν this follows immediately by the fact that X ∈ IE and the class IE is IB-weakly-hereditary-separated. keywords: dm ik; ib ie cache: agt-1652.pdf plain text: agt-1652.txt item: #137 of 431 id: agt-1653 author: Romaguera, Salvador title: Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces date: 2011-10-01 words: 3326 flesch: 78 summary: [10] R. Heckmann, Approximation of metric spaces by partial metric spaces, Applied Cate- gorical Structures 7 (1999), 71–83. 2010 MSC: 54H25, 47H10, 54E50 Keywords: Matkowski’s fixed point theorem; Generalized contraction; 0- complete partial metric space; Ordered partial metric space 1. keywords: metric cache: agt-1653.pdf plain text: agt-1653.txt item: #138 of 431 id: agt-1654 author: Elser, Stefan Ottmar title: Density of k-Box-Products and the existence of generalized independent families date: 2011-10-01 words: 1994 flesch: 88 summary: ∅.Let p ∈ W be an point so that prji(p) ∈ fji(xi) for all ν ≤ Obviously there is a set D whi h is dense in �κi∈IXi and |pri(D)| ≤ µfor all i ∈ I.Let �κi∈IWi be the κ-box-produ t of dis rete spa es Wi with |Wi| = µ andlet f : ∏i∈I Wi → D be a ontinuous and surje tive fun tion. keywords: produ cache: agt-1654.pdf plain text: agt-1654.txt item: #139 of 431 id: agt-16562 author: Karapinar, Erdal title: Revisiting Ciric type nonunique fixed point theorems via interpolation date: 2021-12-09 words: 5119 flesch: 85 summary: 22, no. 2 (2021), 483-496 doi:10.4995/agt.2021.16562 © AGT, UPV, 2021 Revisiting Ćirić type nonunique fixed point theorems via interpolation Erdal Karapınar * Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh, Vietnam Department of Mathematics, Cankaya University 06836, Incek, Ankara-Turkey. If there is ψ ∈ Ψ and α ∈ (0, 1) such that (2.3) min{ ( dα(Tx,Ty)d1−α(x,Tx) ) , ( dα(Tx,Ty)d1−α(y,Ty) ) } −min{dα(x,Ty),d1−α(Tx,y)}≤ ψ(d(x,y)), for all x,y ∈ X, then, for each x0 ∈ X the sequence {Tnx0}n∈N converges to a fixed point of T . Proof. keywords: metric cache: agt-16562.pdf plain text: agt-16562.txt item: #140 of 431 id: agt-16655 author: Boxer, Laurence title: Remarks on fixed point assertions in digital topology, 5 date: 2022-10-03 words: 4049 flesch: 73 summary: 23, no. 2 (2022), 437-451 doi:10.4995/agt.2022.16655 © AGT, UPV, 2022 Remarks on fixed point assertions in digital topology, 5 Laurence Boxer Department of Computer and Information Sciences, Niagara University, Niagara University, NY 14109, USA; and Department of Computer Science and Engineering, State University of New York at Buffalo, USA (boxer@niagara.edu) Communicated by S. Romaguera Abstract As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in “digital metric spaces” - assertions that are incorrect or incorrectly proven, or reduce to triviality. E.g., in many cases, functions that satisfy fixed point assertions must be constant or fail to be digitally continuous [6, 3, 4]. keywords: assertion; digital; figure; metric; point cache: agt-16655.pdf plain text: agt-16655.txt item: #141 of 431 id: agt-16701 author: Abbas, Mujahid; Anjum, Rizwan; Riasat, Shakeela title: Fixed point results of enriched interpolative Kannan type operators with applications date: 2022-10-03 words: 5715 flesch: 70 summary: [18] E. Connell, Properties of fixed point spaces, Proc. To highlight an involvement of parameters a,b and α in (2.1), we call T a (a,b,α)-enriched interpolative Kannan type operator. keywords: contraction; interpolative; kannan; operator; point; space; type cache: agt-16701.pdf plain text: agt-16701.txt item: #142 of 431 id: agt-1671 author: Milani, Vida; Mansourbeigi, Seyed M.H. title: Discrete dynamics on noncommutative CW complexes date: 2013-09-18 words: 5789 flesch: 83 summary: And eventually from the lemma (4.4), for all I,J ∈ Prim(A) we have J ∈ Θ(I,1) = F(I) J ⊇ I}, and an open set OI := {J ∈ Prim(A) : keywords: complexes; noncommutative; prim(a cache: agt-1671.pdf plain text: agt-1671.txt item: #143 of 431 id: agt-16720 author: Gupta, Ankit; Sarma, Ratna Dev title: A Urysohn lemma for regular spaces date: 2022-10-03 words: 5080 flesch: 87 summary: 23, no. 2 (2022), 243-253 doi:10.4995/agt.2022.16720 © AGT, UPV, 2022 A Urysohn lemma for regular spaces Ankit Gupta a and Ratna Dev Sarma b a Department of Mathematics, Bharati College, (University of Delhi), Delhi 110058, India (ankitsince1988@yahoo.co.in) b Department of Mathematics, Rajdhani College (University of Delhi), Delhi 110015, India (ratna sarma@yahoo.com) Communicated by S. Garćıa-Ferreira Abstract Using the concept of m-open sets, M-regularity and M-normality are introduced and investigated. The following example gives an idea about the abundance of m-open sets. keywords: set; space cache: agt-16720.pdf plain text: agt-16720.txt item: #144 of 431 id: agt-16783 author: Asim, Mohammad; Kumar, Santosh; Imdad, Mohammad; George, Reny title: C*-algebra valued quasi metric spaces and fixed point results with an application date: 2022-10-03 words: 5366 flesch: 88 summary: Define d : A×A →A by (for all a,b ∈ A): d(a,b) =   [ b−a 0 0 k(b−a) ] The associated C∗-algebra valued quasi metric space open ball of radius � centered at a B� = {b ∈ A : ds(a,b) ≺ �}. keywords: c∗-algebra; d(a; metric; space cache: agt-16783.pdf plain text: agt-16783.txt item: #145 of 431 id: agt-16925 author: Kumar, Mandeep; Tyagi, Brij Kishore title: Cardinal invariants and special maps of quasicontinuous functions with the topology of pointwise convergence date: 2022-10-03 words: 6252 flesch: 92 summary: ,yn ∈ Y . Then for any x ∈ X, any nonempty closed set F ⊆ X such that x /∈ F and y1,y2 ∈ Y , there exists a quasicontinuous function f : keywords: qp(x; space cache: agt-16925.pdf plain text: agt-16925.txt item: #146 of 431 id: agt-16940 author: Ammar, Aymen; Fakhfakh, Slim; Jeribi, Aref title: Fredholm theory for demicompact linear relations date: 2022-10-03 words: 4465 flesch: 79 summary: Subsequently, we shall exhibit some results on Fredholm linear relations and upper semi-Fredholm demicompact lin- ear relations. In section 3 which is entitled ”Fredholm and upper semi-Fredholm linear relations”, we investigate Fredholm linear relations as well as upper semi- Fredholm demicompact linear relations (see Theorems 3.1 and 3.2). keywords: demicompact; linear cache: agt-16940.pdf plain text: agt-16940.txt item: #147 of 431 id: agt-1695 author: Alas, Ofelia T.; Wilson, Richard G. title: The structure of the poset of regular topologies on a set date: 2011-04-01 words: 6895 flesch: 78 summary: If x 6= z ∈ U ∈ τ, then there is some τ-closed neighbourhood W ⊆ U of z and some n ∈ ω such that W ∩ ⋃ {Unm : m ∈ ω} = ∅ and hence W is a µA-closed neighbourhood of z contained in U. Thus (X,µA) is regular. However, if for some n0 ∈ ω, Un \ clσ(W) = ∅ for all n ≥ n0, then pn ∈ Un ⊆ clσ(W) for all n ≥ n0 contradicting the fact that pn ∈ X \ U ⊆ X \ clσ(W). keywords: regular; topology cache: agt-1695.pdf plain text: agt-1695.txt item: #148 of 431 id: agt-1696 author: Ruza, Luz M.; Vielma, Jorge title: The equality of the Patch topology and the Ultrafilter topology: A shortcut date: 2011-04-01 words: 639 flesch: 76 summary: Keywords: Patch topology, ultrafilter topology, prime spectrum of a ring. (Received November 2008 – Accepted September 2009) Luz M. Ruza (ruza@ula.ve) Universidad de los Andes, Departamento de Matemática, Merida, Venezuela Jorge Vielma (vielma@ula.ve) Universidad de los Andes, Departamento de Matemática, Merida, Venezuela The equality of the Patch topology and the[0.2cm] Ultrafilter topology: A shortcut. keywords: topology cache: agt-1696.pdf plain text: agt-1696.txt item: #149 of 431 id: agt-1698 author: Banakh, Taras; Guran, Igor; Ravsky, Alex title: Characterizing meager paratopological groups date: 2011-04-01 words: 3050 flesch: 72 summary: (1l) Assume that U ⊂ G is a non-empty open left P-small subset. Given a subset U ⊂ G, by induction define subsets (±U )n and (∓U )n, n ∈ ω, of G letting (±U )0 keywords: group; paratopological cache: agt-1698.pdf plain text: agt-1698.txt item: #150 of 431 id: agt-1700 author: Neira U., Clara M. title: A Kuratowski-Mrówka type characterization of fibrewise compactness date: 2011-04-01 words: 2937 flesch: 79 summary: F ∈ F} converges to the point t. A tied ultrafilter to the point t or a t-ultrafilter, is a maximal t-filter. = {F ⋃ {ω} : F ∈ F}. keywords: fibrewise cache: agt-1700.pdf plain text: agt-1700.txt item: #151 of 431 id: agt-17006 author: Alghamdi, Ohud; Kalantan, Lutfi title: Results about S2-paracompactness date: 2022-10-03 words: 2935 flesch: 76 summary: Conversely, assume that X is S2 paracompact. Moreover, If Y is T2 paracompact, then X is S2-paracompact keywords: paracompact; space cache: agt-17006.pdf plain text: agt-17006.txt item: #152 of 431 id: agt-1701 author: Zvina, Irina title: Introduction to generalized topological spaces date: 2011-04-01 words: 9315 flesch: 88 summary: Since for every element a ∈ G there is U ∈ T such that a ≤ ∨ U, we conclude that G ⊆ sm(G). We say that Y ⊆ X is a neighborhood of a point x iff there is U ∈ T such that x ∈ U ⊆ Y . keywords: space cache: agt-1701.pdf plain text: agt-1701.txt item: #153 of 431 id: agt-1702 author: Hardtke, Jan-David title: Some remarks on stronger versions of the Boundary Problem for Banach spaces date: 2011-04-01 words: 5658 flesch: 84 summary: Let B be a subset of BX∗ that separates the points of X and let (xn)n∈N be a sequence in X as well as x ∈ X and ε ≥ 0. , x ∗ k ∈ BX∗ be arbitrary. keywords: lim; theorem cache: agt-1702.pdf plain text: agt-1702.txt item: #154 of 431 id: agt-17021 author: Singh, Sumit title: On set star-Lindelöf spaces date: 2022-10-03 words: 4038 flesch: 86 summary: [21] W. F. Xuan and W. X. Shi, Notes on star Lindelöf spaces, Topology Appl. The class of set star-Lindelöf spaces lie between the class of Lindelöf spaces and the class of star-Lindelöf spaces. keywords: lindelöf; set; star cache: agt-17021.pdf plain text: agt-17021.txt item: #155 of 431 id: agt-17080 author: Chauhan, Tarun Kumar; Jindal, Varun title: The largest topological ring of functions endowed with the m-topology date: 2022-10-03 words: 2405 flesch: 79 summary: A space X is called a cb-space if for each h ∈ LB(X), there exists f ∈ C(X) such that |h| ≤ f. ∈ RX : |f(x) −g(x)| < �,∀x ∈ X}; (� > 0 is constant) as a base for the neighborhood system at f ∈ RX. keywords: ring; topology cache: agt-17080.pdf plain text: agt-17080.txt item: #156 of 431 id: agt-1711 author: Fenille, Marcio Colombo title: Closed injective systems and its fundamental limit spaces date: 2010-10-01 words: 10352 flesch: 85 summary: = φj (xj ), with xi ∈ Xi and xj ∈ Xj , then we have necessarily xi = φi(xi) for some xi ∈ Xi. keywords: cis; closed; limit; space cache: agt-1711.pdf plain text: agt-1711.txt item: #157 of 431 id: agt-1712 author: Beer, Gerald title: The Alexandroff property and the preservation of strong uniform continuity date: 2010-10-01 words: 8683 flesch: 75 summary: Fix B ∈ B; by uniform convergence on B, choose λB ∈ Λ such that ∀λ � λB, ∀b ∈ B, we have (fλ(b), f (b)) B ∈ B}. keywords: bornology; space; uniform cache: agt-1712.pdf plain text: agt-1712.txt item: #158 of 431 id: agt-1713 author: Günther, Bernd title: Random selection of Borel sets date: 2010-10-01 words: 11259 flesch: 82 summary: A probability measure ν on Y corresponds bijectively to a se- quence of probability measures νn = pnν on I 2n such that pn+1n νn+1 = νn and for all ε > 0 (7.1) lim n→∞ νn { 2−n 2n−1 ∑ m=0 ( xnm − 1 2 )2 ≤ 1 4 − ε } = 0 ν is invariant under G∞ if and only if each νn is invariant under Gn. β − µ (Un) < µ(A) − µ (Un) − µ (Vn). keywords: anm; borel; measure; random; sets; xnm cache: agt-1713.pdf plain text: agt-1713.txt item: #159 of 431 id: agt-1724 author: Sharma, Puneet; Nagar, Anima title: Topological dynamics on hyperspaces date: 2010-04-01 words: 9559 flesch: 79 summary: [8] G. Di Maio and S. A. Naimpally, Some notes on hyperspace topologies, Ricerche Mat. 51, no. 1 (2002), 49–60. If U and V are two open covers of X, define, U ∨ V = {U ⋂ V : U ∈ U, V ∈ V}. keywords: hyperspace; let; map; topology cache: agt-1724.pdf plain text: agt-1724.txt item: #160 of 431 id: agt-1725 author: Karunakaran, V.; Ganesan, C. title: One point compactification for generalized quotient spaces date: 2010-04-01 words: 3097 flesch: 81 summary: The concept of Generalized function spaces which were introduced and studied by Zemanian are further generalized as Boehmian spaces or as generalized quotient spaces in the recent litera- ture. Keywords: Generalized quotient space, compact, locally compact and Haus- dorff, one point compactification. keywords: compact cache: agt-1725.pdf plain text: agt-1725.txt item: #161 of 431 id: agt-1726 author: Kohli, J.K.; Singh, D. title: Between strong continuity and almost continuity date: 2010-04-01 words: 6678 flesch: 75 summary: A union of regular open sets is called δ-open [39]. Further, if in addition f maps regular open sets to regular open sets, then g is an almost completely continuous function. keywords: open; set cache: agt-1726.pdf plain text: agt-1726.txt item: #162 of 431 id: agt-1727 author: Kohli, J.K.; Singh, D.; Kumar, Rajesh; Aggarwal, Jeetendra title: Between continuity and set connectedness date: 2010-04-01 words: 6346 flesch: 78 summary: The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu- ous functions studied by Long and Herrignton (Kyungpook Math. Continuous functions play a prominent role in topology, analysis and many other branches of mathematics. keywords: functions; set cache: agt-1727.pdf plain text: agt-1727.txt item: #163 of 431 id: agt-1732 author: Caterino, Alessandro; Ceppitelli, Rita; Maccarino, Francesca title: Continuous utility functions on submetrizable hemicompact k-spaces date: 2009-10-01 words: 3977 flesch: 63 summary: Continuous utility functions on submetrizable hemicompact k-spaces 189 2. Later (Theorem 4.2) we will extend the Theorem of Levin to the case when X is submetrizable and hemicompact, Continuous utility functions on submetrizable hemicompact k-spaces 193 Γ is metrizable and Γ × X is a k-space. keywords: function; preorder; space; utility cache: agt-1732.pdf plain text: agt-1732.txt item: #164 of 431 id: agt-1733 author: Das, Ananga Kumar title: ∆-normal spaces and decompositions of normality date: 2013-09-30 words: 4588 flesch: 82 summary: Since every continuous function lifts back every θ-open set to θ-open set, the set f −1[0, 1/2) and f −1 (1/2, 1] are disjoint θ-open sets containing A and B respectively. The family of θ-open sets as well as the family of δ open sets form topologies on X. keywords: open; set cache: agt-1733.pdf plain text: agt-1733.txt item: #165 of 431 id: agt-1734 author: González-Silva, R. A.; Hrusák, M. title: More on ultrafilters and topological games date: 2013-09-30 words: 6707 flesch: 88 summary: For each s ∈ 2 <ω inductively pick xs ∈ X and a clopen neighborhood Wn of x, such that xs ∈ σ|s|(〈xs|0 , xs|1 , ..., xs||s|−1〉; 〈V0, ..., V|s|−1〉) = V|s|, xs 6∈ {xr : r ∈ 2 ≤|s| and r 6= s}, xs ∈ Wn for all s ∈ 2 n and xs 6∈ Wn for all s ∈ 2 0. Proof. ∈ X, and ρ′+(y, h, F ) is a subadditive homogenous function in the variable h. Theorem 2.2 in [6] says that whenever y0 is a n.c. point of G to F, ρ′+(y0, y − y0) ≥ 0 for all y ∈ G. In the following, we shall obtain a necessary condition for strong n.c. points. keywords: n.c; point; strong cache: agt-1931.pdf plain text: agt-1931.txt item: #229 of 431 id: agt-1932 author: Zvina, Irina title: On i-topological spaces: generalization of the concept of a topological space via ideals date: 2006-04-01 words: 8347 flesch: 84 summary: Then an i-topology on X is a family T of subsets of X that satisfies the following conditions: (T1) ∅,X ∈ T ; (T2) for any U ⊆ T there exists U ∈ T such that ⋃ U ≈ U; (T3) for any V,W ∈ T there exists U ∈ T such that Suppose we are given an i-topological space (X,T ,I) and a subset M ⊆ X. We will use the following notations: T |M = { M ∩ U | U ∈ T and M ∩ U /∈ keywords: space; topological cache: agt-1932.pdf plain text: agt-1932.txt item: #230 of 431 id: agt-1933 author: Arhangelskii, A. V.; Uspenskij, Vladimir V. title: Topological groups: local versus global date: 2006-04-01 words: 2354 flesch: 69 summary: Secondary: 54020, 54D60, 54E15 Keywords: topological group, paracompact, Lindelöf, local properties 1. For topological groups, Ty- chonoff is equivalent to Hausdorff. keywords: group; space cache: agt-1933.pdf plain text: agt-1933.txt item: #231 of 431 id: agt-1934 author: Raphael, R.; Woods, R.G. title: On RG-spaces and the regularity degree date: 2006-04-01 words: 16488 flesch: 90 summary: A point p ∈ X is called a very weak P-point if p is not a limit point of any countable discrete subset of X. Let F ∈ PF(X) and define α(F) keywords: c(x; clopen; g(x; prime; proof; set; space cache: agt-1934.pdf plain text: agt-1934.txt item: #232 of 431 id: agt-1936 author: Comfort, W. W.; Raczkowski, S. U.; Trigos-Arrieta, F. J. title: Making group topologies with, and without, convergent sequences date: 2006-04-01 words: 8187 flesch: 80 summary: By [22] (9.8) for every (Hausdorff) locally compact Abelian compactly generated group G there are non-negative integers m and n and a compact Abelian group K such that G is of the form It follows that a non-discrete (Hausdorff ) locally compact Abelian compactly generated group G has 2|G|-many dense non-Haar- measurable subgroups of both cardinality and index |G|. keywords: abelian; compact; group; infinite; sequence; subgroup; theorem; topologies cache: agt-1936.pdf plain text: agt-1936.txt item: #233 of 431 id: agt-1937 author: Shah, Sejal; Das, T.K. title: On nearly Hausdorff compactifications date: 2006-04-01 words: 2562 flesch: 81 summary: The family of all r-ultrafilters in X is denoted by rX. Observe that for x ∈ X, there exists a unique r-ultrafilter αx in rX such that ∩αx = {x}. The resulting space X is a non Hausdorff, nh-space without property Π. keywords: space cache: agt-1937.pdf plain text: agt-1937.txt item: #234 of 431 id: agt-1938 author: Song, Yan-Kui title: On spaces with the property (wa) date: 2006-04-01 words: 3375 flesch: 87 summary: The underlying set of A(X) is X × {0, 1}; each point of X × {1} is isolated and a basic neighborhood of a point 〈x, 0〉 ∈ X × {0} is the set of the form (U × {0}) ∪ ((U × {1}) \ {〈x, 1〉}), where U is a neighborhood of x in X. Theorem 3.6. Then, U0 = {f −1(U ) : U ∈ U} is an open cover of X and D0 = f −1(D) is dense in X since f is varpseudocompact. keywords: property; space cache: agt-1938.pdf plain text: agt-1938.txt item: #235 of 431 id: agt-1950 author: Barton, Bill; Lichtenberk, Frank; Reilly, Ivan L. title: The language of topology: a Turkish case study date: 2005-10-01 words: 5012 flesch: 54 summary: What are the differences in the language of topology when it is expressed in English, Spanish, Mandarin, Czech or Turkish? Does topology itself change when expressed in different languages? It thus provides an ideal field in which to investigate the influence (if any) of different languages on the development of mathema- tical concepts. keywords: english; general; language; mathematical; meaning; research; space; term; topology; turkish; use; word cache: agt-1950.pdf plain text: agt-1950.txt item: #236 of 431 id: agt-1951 author: Ganster, Maximilian; Georgiou, D. N.; Jafari, S.; Moshokoa, S. P. title: On some applications of fuzzy points date: 2005-10-01 words: 7406 flesch: 94 summary: By using the notion of fuzzy set, Wong (see [15]) was able to introduce and investigate the notions of fuzzy points. The purpose of this paper is to give some applications of fuzzy points in fuzzy topo- logical spaces. keywords: pre; set cache: agt-1951.pdf plain text: agt-1951.txt item: #237 of 431 id: agt-1952 author: Garcia-Raffi, Lluís M.; Sánchez-Pérez, E. A. title: Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators date: 2005-10-01 words: 3710 flesch: 67 summary: [9] F. Mart́ınez-Giménez and E. A. Sánchez-Pérez, Vector measure range duality and fac- torizations of (D, p)-summing operators from Banach function spaces, Bull. Introduction Compactness of the unit ball of Banach spaces is a useful tool in the theory of operators between these spaces. keywords: banach; lq(m; measure; spaces; theorem; vector cache: agt-1952.pdf plain text: agt-1952.txt item: #238 of 431 id: agt-1956 author: Sánchez-Álvarez, José Manuel title: On semi-Lipschitz functions with values in a quasi-normed linear space date: 2005-10-01 words: 5399 flesch: 94 summary: The complexity quasi-metric space was introduced in [16] to study comple- xity analysis of programs. Our basic reference for quasi-metric spaces is [4]. keywords: d(x; quasi; sl0(d cache: agt-1956.pdf plain text: agt-1956.txt item: #239 of 431 id: agt-1957 author: Valero, Oscar title: On Banach fixed point theorems for partial metric spaces date: 2005-10-01 words: 4619 flesch: 85 summary: In this paper we extend the notion of contraction between partial metric spaces to the dualistic partial metric context, and present two generalizations and one “local version” of the Banach fixed point theorem given in ([14]), which recuperate the several well-known classical fixed point theorems when the dualistic partial metric converts into a metric. 2. Contractions on dualistic partial metric spaces For the following discussion we recall some basics correspondences between dualistic partial metrics and quasi-metric spaces. x ∈ X, ε > 0}, where Bd(x,ε) = {y ∈ X : d(x,y) < ε} for all x ∈ X and ε > 0. keywords: metric; point cache: agt-1957.pdf plain text: agt-1957.txt item: #240 of 431 id: agt-1958 author: Bella, Angelo title: Remarks on the finite derived set property date: 2005-04-01 words: 2704 flesch: 74 summary: It is easy to check that the map f → xf is injective and consequently |X| ≥ c. � The previous construction with some minor modifications provides a better result for Lindelöf spaces. For the converse inequality, let λ < h and let {Xα : α < λ} be a family of SC spaces with the FDS property. keywords: fds; infinite; property; set; space cache: agt-1958.pdf plain text: agt-1958.txt item: #241 of 431 id: agt-1959 author: Benkafadar, Nasreddine Mohamed; Benkara-Mostefa, M. C. title: A generalized coincidence point index date: 2005-04-01 words: 5798 flesch: 78 summary: Ig ·O{θ}, where i : U −→ En is the natural injection. Let F : U −→ K(En) be a multi-valued mapping and K be a compact subset of U ⊆ En. keywords: u\k cache: agt-1959.pdf plain text: agt-1959.txt item: #242 of 431 id: agt-1960 author: Kohli, J.K.; Das, A.K. title: On functionally θ-normal spaces date: 2005-04-01 words: 6521 flesch: 76 summary: The resulting characterizations are then used to investigate the interrelations that exist among certain gene- ralizations of normal spaces such as (weakly) (functionally) θ-normal spaces, δ-normal spaces defined by Mack [10], δ-normally separated spaces initiated by Mack [10] and Zenor It turns out that the set Auθ is the smallest θ-closed set containing A. On functionally θ-normal spaces 3 Definition 2.5 ([2]). keywords: open; set; sets; space cache: agt-1960.pdf plain text: agt-1960.txt item: #243 of 431 id: agt-1961 author: Nickolas, Peter; Tkachenko, Mikhail title: The character of free topological groups I date: 2005-04-01 words: 14268 flesch: 83 summary: ∈ C(U)} is dense in (U, ⊆), let U ∈ U and take V ∈ U which is symmetric and satisfies 2V ⊆ U. Then for every uniformly con- tinuous pseudometric d on (X, U) the set Vd is open in A(X, U), and for every neighborhood U of the neutral element in A(X, U) there exists a uniformly con- tinuous pseudometric d on (X, U) such that Vd ⊆ U. Instead of using uniformly continuous pseudometrics, one can directly use the entourages U ∈ U belonging to a uniform space (X, U) to construct a neighborhood base at the identity of A(X, U). keywords: free; group; n u; set; space; theorem; topological; uniform cache: agt-1961.pdf plain text: agt-1961.txt item: #244 of 431 id: agt-1962 author: Nickolas, Peter; Tkachenko, Mikhail title: The character of free topological groups II date: 2005-04-01 words: 7066 flesch: 82 summary: In this sequel to [11], we specifically investigate the characters of the free and free abelian topological groups on metrizable spaces and on compact spaces, and on certain closely related spaces, obtaining more detailed information in both cases than was available in [11]. Also, the principal results were obtained with- out the imposition of strong uniform or topological conditions on the given spaces, though numerous corollaries were derived at various points for metriz- able spaces, compact spaces and other classes of spaces. keywords: corollary; free; groups; space; χ(a(x cache: agt-1962.pdf plain text: agt-1962.txt item: #245 of 431 id: agt-1964 author: Cao, Jiling; Ganster, Maximilian; Reilly, Ivan L.; Steiner, Markus title: δ-closure, θ-closure and generalized closed sets date: 2005-04-01 words: 3266 flesch: 87 summary: [7] J. Dontchev and H. Maki, On θ-generalized closed sets, Internat. We study some new classes of generalized closed sets (in the sense of N. Levine) in a topological space via the associated δ-closure and θ-closure. keywords: closed cache: agt-1964.pdf plain text: agt-1964.txt item: #246 of 431 id: agt-1966 author: Neira U., Clara M.; Varela, Januario title: On separation axioms of uniform bundles and sheaves date: 2004-10-01 words: 8972 flesch: 85 summary: By the semicontinuity hypothesis the sets {s ∈ B : di(ξ(s),α(s)) < δj} are open, it follows that S = P ∩ Q ∩ {s ∈ B : di(ξ(s),α(s)) keywords: space cache: agt-1966.pdf plain text: agt-1966.txt item: #247 of 431 id: agt-1967 author: Herden, Gerhard; Pallack, Andreas title: On the cardinality of indifference classes date: 2004-10-01 words: 9120 flesch: 73 summary: Let x, y ∈ X be different points. Let, therefore, two different points x, y ∈ X be arbitrarily chosen. keywords: indifference; total cache: agt-1967.pdf plain text: agt-1967.txt item: #248 of 431 id: agt-1971 author: Candeal, Juan C.; Induráin, Esteban; Zudaire, M. title: Continuous representability of interval orders date: 2004-10-01 words: 8269 flesch: 68 summary: {y ∈ X : y ≺ x} and U(x) = {y ∈ X : x ≺ y} are called, respectively, the lower contour set and the upper contour set relative to ≺. Continuous representability of interval orders 215 Definition 2.1. An interval order ≺ on a set X is said to be i.o.-separable if there exists a countable subset D ⊆ X such that for every x, y ∈ X with x ≺ y there exists an element d in D such that x ≺ d -∗∗ y. keywords: interval; order cache: agt-1971.pdf plain text: agt-1971.txt item: #249 of 431 id: agt-1972 author: Alas, Ofelia T.; Wilson, Richard G. title: Which topologies can have immediate successors in the lattice of T1-topologies? date: 2004-10-01 words: 6914 flesch: 74 summary: Suppose that p ∈ X is not isolated. A point p ∈ X is a maximal point if and only if the trace of the open neighbourhood filter at p on the subspace X \{p} is an open ultrafilter. keywords: point; topology cache: agt-1972.pdf plain text: agt-1972.txt item: #250 of 431 id: agt-1973 author: Dow, Alan; Porter, Jack R.; Stephenson, R.M.; Grant Woods, R. title: Spaces whose Pseudocompact Subspaces are Closed Subsets date: 2004-10-01 words: 12069 flesch: 79 summary: [9] Zhou Hao-Xuan, “A conjecture on compact Fréchet spaces”, Proc. We recall that the adherence of a filter base F on a space X is the intersection of the closures of the members of F, and by a cluster point of a sequence {Un : n ∈ N} of subsets of a space X is meant a point p ∈ X such that for every neighborhood V of p, V ∩ Un 6= ∅ for infinitely many integers n. keywords: closed; fcc; point; sequence; space; subset cache: agt-1973.pdf plain text: agt-1973.txt item: #251 of 431 id: agt-1974 author: Sequeira, Luís title: Two transfinite chains of separation conditions between T1 and T2 date: 2004-10-01 words: 3597 flesch: 76 summary: 266 Lúıs Sequeira Here, we consider these separation conditions for topological spaces in gen- eral, and describe their strengths, relative to each other and to the well known conditions of sobriety and the Ti axioms. All H and all sH conditions are distinct The purpose of this section is to provide examples of topological spaces that show that the H and sH conditions are all distinct from each other (apart from the noted equivalence H1 ⇔ sH1 ⇔ T2). keywords: space cache: agt-1974.pdf plain text: agt-1974.txt item: #252 of 431 id: agt-1991 author: Kim, Junhui title: Iterated starcompact topological spaces date: 2004-04-01 words: 5200 flesch: 84 summary: Let O = {U∩Z : U ∈ U} be a collection of non-empty sets. Let S = R and τ0 be the Euclidean topology on R. Endow S with a new topology τ1 = {U r F : U ∈ τ0, |F | ≤ ω}. keywords: space cache: agt-1991.pdf plain text: agt-1991.txt item: #253 of 431 id: agt-1992 author: Candeal, Juan C.; de Miguel, Juan R.; Induráin, Esteban; Mehta, Ghansyam B. title: Representations of ordered semigroups and the Physical concept of Entropy date: 2004-04-01 words: 6388 flesch: 64 summary: (2) additively representable (respectively: pseudo-representable) if there ex- ists a utility (respectively: pseudo-utility) function u for - that is an homomorphism (i.e.: u(x + y) = u(x) + u(y), for every x, y ∈ S). A positive semigroup (S, +, -) is said to be: (1) Archimedean if for every x, y ∈ S with x ≺ y, there exists n ∈ N such that y ≺ n · x, (n · x = n times ︷ ︸︸ keywords: cooper; entropy; function; utility cache: agt-1992.pdf plain text: agt-1992.txt item: #254 of 431 id: agt-1993 author: Banak, Taras; Zdomskyi, Lubomyr title: The topological structure of (homogeneous) spaces and groups with countable cs∗-character date: 2004-04-01 words: 12829 flesch: 74 summary: The class of topological spaces with countable cs∗-character is closed under many topological operations and contains all ℵ-spaces and all spaces with point-countable cs∗-network. Introduction In this paper we introduce and study three new local cardinal invariants of topological spaces called the sb-character, the cs-character and cs∗-character, and describe the structure of sequential topological groups with countable cs∗- character. keywords: compact; convergent; countable; point; sequence; sequential; space; topology cache: agt-1993.pdf plain text: agt-1993.txt item: #255 of 431 id: agt-1994 author: Moreno, Samuel G.; Almira, Jose María; García-Caballero, Esther M.; Quesada, J.M. title: A topological approach to Best Approximation Theory date: 2004-04-01 words: 9701 flesch: 83 summary: Let C be a closed bounded convex subset of a Banach space X which has the origin as an interior point and let fC denote the Minkowski functional with respect to C. Given a nonempty closed bounded subset A ⊂ X and a point x ∈ X, we consider the minimization problem which consists in proving the existence of a point a0 ∈ A such that fC(a0 − x) = inf{fC(a [0, ∞) into the power set P(X) that fulfills the axioms (iii) and (iv) of the above definition, then it is called a pre–wrapping for X. Fixed a wrapping ξ for X, A a nonempty subset of X and x ∈ X, we define: • the radius set of the ξ-balls of center x with nonempty intersection with A (2.1) Fξ(x, A) = {r ≥ 0 keywords: function; space cache: agt-1994.pdf plain text: agt-1994.txt item: #256 of 431 id: agt-1995 author: Gutev, Valentin; Nogura, Tsugunori title: Some problems on selections for hyperspace topologies date: 2004-04-01 words: 4284 flesch: 74 summary: A topology τ on F(X, T ) is called admissible (see [18]) if its restriction on the set of all singletons {{x} : x ∈ X} of X coincides with the topology T . The concept of a τ-continuous selection Let (X, T ) be a T1-space, where T is the topology of X, and let F(X, T ) be the set of all non-empty closed (with respect to T ) subsets of X. keywords: f(x; space cache: agt-1995.pdf plain text: agt-1995.txt item: #257 of 431 id: agt-1996 author: Bonanzinga, Maddalena; Cammaroto, F.; Kocinac, Ljubisa D.R. title: Star-Hurewicz and related properties date: 2004-04-01 words: 5340 flesch: 83 summary: Then: (a) The symbol S∗1(A, B) denotes the selection hypothesis: for each sequence (Un : n ∈ N) of elements of A there exists a sequence (Un : n ∈ N) such that for each n, Un ∈ Un and {St(Un, Un) : n ∈ N} is an element of B; (b) The symbol S∗fin(A, B) denotes the selection hypothesis: for each se- quence (Un : n ∈ N) of elements of A there is a sequence (Vn : n ∈ N) such that for each n ∈ N, Vn is a finite subset of Un, and ⋃ n∈N{St(V, Un) : that for each sequence (Un : n ∈ N) of elements of A there exists a sequence (Un : n ∈ N) such that for each n, Un ∈ Un and {Un : keywords: open; sequence; star cache: agt-1996.pdf plain text: agt-1996.txt item: #258 of 431 id: agt-1998 author: Castro Pereira, I.; Tomita, A.H. title: A countably compact free Abelian group whose size has countable cofinality date: 2004-04-01 words: 2421 flesch: 84 summary: Note that r = (α,{xr,ξ : ξ ∈ Dr},{Ar,ζ : ζ ∈ Er}) may not be a condition in P but it can be extended to a condition p by applying Lemma 4.1. ξ is an accumulation point of {xp,Fζ(n) : n ∈ ω} for each ξ ∈ Ap,ζ and each ζ ∈ Ep; viii) {xp,ξ : ξ ∈ Dp} is a faithfully indexed free set. keywords: group cache: agt-1998.pdf plain text: agt-1998.txt item: #259 of 431 id: agt-1999 author: Acharyya, Sudip Kumar; Chattopadhyaya, K. C.; Ghosh, Partha Pratim title: Continuous functions with compact support date: 2004-04-01 words: 4860 flesch: 73 summary: ∈ F with the constant function X t −→ F , de- fined by t : x 7→ t, then one easily gets F ⊆ C∗(X, F) ⊆ B(X, F) ⊆ C(X, F). It is easily seen that the units of C(X, F) are precisely those continuous functions X f −→ F that do not vanish anywhere, i.e., with ZX,F (f) = ∅. keywords: ck(x; theorem cache: agt-1999.pdf plain text: agt-1999.txt item: #260 of 431 id: agt-2000 author: Kopperman, Ralph D.; Matthews, S.; Pajoohesh, H. title: Partial metrizability in value quantales date: 2004-04-01 words: 7367 flesch: 82 summary: = {a|(∃x ∈ I,y ∈ J ∈ S ∪ {⊤})(a ≥ x ⋆ y)} = ⋃ J∈S∪{⊤}{a|(∃x ∈ I,y ∈ J)(a ≥ (a) Notice that U ∈ α(≥τ) if and only if x ∈ U and y ∈ cl({x}) imply that y ∈ U. Now consider x ∈ T ∈ τ then define f : (X,τ,α(≥τ)) → (IB,σ,ω) such that f = ∞ on T and f = 0 on X \T . keywords: p(x cache: agt-2000.pdf plain text: agt-2000.txt item: #261 of 431 id: agt-2001 author: Gregori, Valentín; Romaguera, Salvador title: Fuzzy quasi-metric spaces date: 2004-04-01 words: 3928 flesch: 80 summary: In this paper, we introduce two notions of fuzzy quasi-metric space that generalize the corresponding notions of fuzzy metric space by Kramosil and Michalek, and by George and Veeramani to the quasi-metric context. With the help of these results one can easily derive many properties of fuzzy quasi-metric spaces. keywords: fuzzy; metric; quasi cache: agt-2001.pdf plain text: agt-2001.txt item: #262 of 431 id: agt-2005 author: Baran, Mehmet; Kula, Muammer title: A note on separation and compactness in categories of convergence spaces date: 2003-04-01 words: 6924 flesch: 84 summary: F ⊂ B is strongly closed iff for any a ∈ B with a 6∈ F , [a] 6∈ L(c) for all c ∈ F and α∪ F ⊂ B is closed iff for any a 6∈ F , if there exists α ∈ L(a) such that α∪ keywords: iff cache: agt-2005.pdf plain text: agt-2005.txt item: #263 of 431 id: agt-2006 author: Claes, Veerle; Sonck, G. title: The quasitopos hull of the construct of closure spaces date: 2003-04-01 words: 4508 flesch: 77 summary: For a preclosure space (X, cl) and x ∈ X, the collection of neighbor- hoods V(x) = {V ⊂ X | x /∈ cl (X\V )} satisfies the following three conditions: (V1) X ∈V(x), (V2) ∀V ∈V(x) : Now suppose A0 ∈ A and αA0 66 α0. keywords: construct; hull cache: agt-2006.pdf plain text: agt-2006.txt item: #264 of 431 id: agt-2007 author: Deses, D.; Giuli, Eraldo; Lowen-Colebunders, E. title: On complete objects in the category of T0 closure spaces date: 2003-04-01 words: 4509 flesch: 75 summary: (3) To see the naturality of η, consider continuous f : X → Y where X and Y are complete T0 closure spaces. For V the class of epi- morphic embeddings in the construct Cl0 of T0 closure spaces we prove that the class of V-injective objects is the unique firmly V-reflective subconstruct of Cl0. keywords: cl0; closure; complete cache: agt-2007.pdf plain text: agt-2007.txt item: #265 of 431 id: agt-2008 author: Yalvaç, T.H. title: On φ 1,2-countable compactness and filters date: 2003-04-01 words: 5641 flesch: 88 summary: We say that: (a) F, ϕ1,2-accumulates to a, if a ∈ ⋂ {ϕ1,2cl F | F ∈F} [20]. (b) F, ϕ1,2-converges to a, if for each U ∈ ϕ1O(X,a), there exists F ∈ F such that F ⊆ ϕ2(U) There exists an a ∈ A such that a ∈ ⋂ {ϕ1,2cl F | F ∈ F} and a Ua ∈ U such that a ∈ Ua. keywords: set; ϕ1,2; ϕ1o(x cache: agt-2008.pdf plain text: agt-2008.txt item: #266 of 431 id: agt-2009 author: Waszkiewicz, Pawel title: The local triangle axiom in topology and domain theory date: 2003-04-01 words: 10268 flesch: 78 summary: For x,y ∈ X, x v/τρy iff x /∈ cl{y} iff ∃ε > 0. Then for all x,y ∈ X, x vτρ y iff ρ(x,y) = ρ(x,x). keywords: distance; semimetric; topology; ρ(x cache: agt-2009.pdf plain text: agt-2009.txt item: #267 of 431 id: agt-2011 author: Mucuk, Osman; Icen, Ilhan title: Holonomy, extendibility, and the star universal cover of a topological groupoid date: 2003-04-01 words: 5547 flesch: 74 summary: Then M admits a unique structure of topological groupoid such that W ′ is an open subset and p : M → Q is a morphism of topological groupoids mapping W ′ homeomorphically to W . Proof. Then the groupoid MG constructed above may be given a structure of topological groupoid such that each star (MG)x is a universal cover of Gx and W is isomorphic to an open subset W̃ of MG. Proof. keywords: groupoid; topology cache: agt-2011.pdf plain text: agt-2011.txt item: #268 of 431 id: agt-2012 author: Brümmer, Guillaume C.L.; Sioen, M. title: Functorial approach structures date: 2003-04-01 words: 2549 flesch: 65 summary: We show that there exists at least a proper class of functorial approach structures, i.e., right inverses to the forgetful func- tor T : AP → Top (where AP denotes the topological construct of approach spaces and contractions as introduced by R. Lowen). Keywords: Approach space, (approach) bicompleteness, epireflective sub- category, functorial approach structure, spanning, topological space. keywords: approach; functorial; quasi; spaces cache: agt-2012.pdf plain text: agt-2012.txt item: #269 of 431 id: agt-2013 author: Burdick, Bruce S. title: On the use of partial orders in uniform spaces date: 2003-04-01 words: 7048 flesch: 78 summary: For a fixed uniform space (X,U) and a possibly different uniformity U∗ on X, the following are equivalent: (1) Any open Cauchy ponet for U is open Cauchy for U∗. (2) Any dense Cauchy ponet for U is dense Cauchy for U∗. Partial orders in uniform spaces 113 (3) U∗ ⊆U. Proof. For a fixed uniform space (X,U) and a possibly different uniformity U∗ on X, the following are equivalent: (1) Any ponet which is open dense Cauchy for U is open dense Cauchy for U∗. (2) Any net which is Cauchy for U is Cauchy for U∗. (3) Any filter which is Cauchy for U is Cauchy for U∗. (4) keywords: cauchy; dense; space; uniform cache: agt-2013.pdf plain text: agt-2013.txt item: #270 of 431 id: agt-2014 author: Brattka, Vasco title: Effective representations of the space of linear bounded operators date: 2003-04-01 words: 8224 flesch: 70 summary: [δn,δ]. To make this paper as self-contained as possible, we will discuss some basic facts on computable metric spaces and computable Banach spaces in the follow- ing section. Computable Metric and Banach Spaces In this section we will briefly discuss computable metric spaces and com- putable Banach spaces. keywords: computable; graph; metric; operator; representations; space; δev cache: agt-2014.pdf plain text: agt-2014.txt item: #271 of 431 id: agt-2015 author: Kopperman, Ralph D.; Robbie, D. title: Skew compact semigroups date: 2003-04-01 words: 4250 flesch: 73 summary: Skew compact spaces are the best behaving generaliza- tion of compact Hausdorff spaces to non-Hausdorff spaces. They have recently become important in computer science, as well as topology, since they are the spaces needed to approximate compact Hausdorff spaces with finite T0 (rarely T2) spaces. keywords: compact cache: agt-2015.pdf plain text: agt-2015.txt item: #272 of 431 id: agt-2016 author: Giuli, Eraldo title: On classes of T0 spaces admitting completions date: 2003-04-01 words: 6028 flesch: 73 summary: Let k : X → Y be a z-dense embedding with X,Y ∈ X and let f : Y → Ŝ any affine map. Section 5 contains the main result: a class of separated affine sets admits completions whenever it is the class of all separated affine sets of a subcategory of SSET which is stable under affine subsets, disjoint unions and quotients (i.e., of a hereditary coreflective subcategory of SSET). keywords: affine; set; spaces cache: agt-2016.pdf plain text: agt-2016.txt item: #273 of 431 id: agt-2017 author: Ozcag, Selma; Brown, Lawrence M. title: Di-uniform texture spaces date: 2003-04-01 words: 18957 flesch: 87 summary: Then we have s,u ∈ S so that P (s,u) 6⊆ d(D) and there exists t ∈ S satisfying d(C) 6⊆ Q(s,t) and d(C) Then we have s,t ∈ S satisfying P (s,t) 6⊆ d◦d for which we have z ∈ S[ satisfying d[z] 6⊆ Qt and Ps 6⊆ D[z]. keywords: proof; ps 6⊆ cache: agt-2017.pdf plain text: agt-2017.txt item: #274 of 431 id: agt-2018 author: Escardó, Martín title: Injective locales over perfect embeddings and algebras of the upper powerlocale monad date: 2003-04-01 words: 3963 flesch: 66 summary: This is an extension of the equivalence of the category of perfect maps of spectral spaces with that of monotone continuous maps of ordered Stone spaces, previously established by Priestley [21]. Preliminaries We take the basic notions concerning locales and frames for granted [14] – we just emphasize that the category Loc of continuous maps of locales is defined to be the opposite of the category Frm of homomorphisms of frames. keywords: locales; map; monad cache: agt-2018.pdf plain text: agt-2018.txt item: #275 of 431 id: agt-2019 author: Ramkumar, Solai title: Hausdorff connectifications date: 2014-04-01 words: 4514 flesch: 82 summary: If f is an open mapping on every saturated subset of X and f seperates open subsets of X, then f is a connected mapping. Proof. Since f is an open mapping on every saturated subset of X, f(V ) and f(X\V ) are open subsets of Y . keywords: mapping; subset cache: agt-2019.pdf plain text: agt-2019.txt item: #276 of 431 id: agt-2025 author: Naimpally, Somashekhar title: Multivalued function spaces and Atsuji spaces date: 2003-10-01 words: 3531 flesch: 78 summary: Those interested in more details are referred to [3] for hypertopologies, [21] for proximities, [17] and [19] for function space topologies. One of the most valuable results in function space topologies for single valued functions is the embedding of the range space in the function space via the constant functions. keywords: space; topology; uniform cache: agt-2025.pdf plain text: agt-2025.txt item: #277 of 431 id: agt-2026 author: Hocking, John G. title: Unusual and bijectively related manifolds date: 2003-10-01 words: 2408 flesch: 78 summary: As an addendum to Theorem 1.7 it is interesting to note that there are bi- maps from orientable manifolds to non-orientable ones but not conversely. I asked myself ”Are there manifolds which admit of a continuous bijection with a discontinuous inverse?” keywords: manifolds cache: agt-2026.pdf plain text: agt-2026.txt item: #278 of 431 id: agt-2027 author: Künzi, Hans-Peter A. title: Transitivity of hereditarily metacompact spaces date: 2003-10-01 words: 2365 flesch: 77 summary: A regular topological space X is said to be a monotonic β-space [1] if, for each point x ∈ X, there exists a decreasing sequence 〈Bn(x)〉n∈ω of open neighborhood bases of X at the point x By Lemma 2.1 there exists a point-finite open cover Gn+1(Un) of Un \O−1(pUn) such that for each Un+1 ∈ Gn+1(Un) there is some point pUn+1 ∈ Un \ O−1(pUn) keywords: finite; point; space cache: agt-2027.pdf plain text: agt-2027.txt item: #279 of 431 id: agt-2028 author: Deses, D.; de Groot-Van der Voorde, A.; Lowen-Colebunders, E. title: Extensions of closure spaces date: 2003-10-01 words: 7708 flesch: 75 summary: The construct of R0 closure spaces is bicoreflectively em- bedded in the construct of seminearness spaces, cfr. 223–241 Extensions of closure spaces D. Deses ∗ , A. De Groot-Van der Voorde, E. Lowen-Colebunders Dedicated to Professor S. Naimpally on the occasion of his 70th birthday. keywords: closure; extension; let; seminearness; space cache: agt-2028.pdf plain text: agt-2028.txt item: #280 of 431 id: agt-2029 author: Ferrer, Jesús title: Quasi-pseudometric properties of the Nikodym-Saks space date: 2003-10-01 words: 4484 flesch: 83 summary: Keywords: quasi-pseudometric space, Nikodym-Saks space. Then, F ∈ Σ(Ω), and, for each n, q∗(F,Fin) = µ(F\Fin) = µ(∪ ∞ j=1(Fij\Fin)) keywords: quasi; space; σ(ω cache: agt-2029.pdf plain text: agt-2029.txt item: #281 of 431 id: agt-2030 author: Kocinac, Ljubisa D.R. title: Closure properties of function spaces date: 2003-10-01 words: 3485 flesch: 82 summary: ,Vn are open in R. For a function f ∈ Ck(X), a compact set K ⊂ X and a positive real number ε we let W(f; K; ε) : Recall that an open cover U of X is called a k-cover if for each compact set K ⊂ X there is a U ∈ U such that keywords: ck(x cache: agt-2030.pdf plain text: agt-2030.txt item: #282 of 431 id: agt-2031 author: Sioen, M.; Verwulgen, S. title: Locally convex approach spaces date: 2003-10-01 words: 6878 flesch: 79 summary: We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convex- ity in the setting of approach vector spaces as introduced in [6]. The purpose of this paper is twofold: we want to put local convexity in the right perspective in the setting of approach vector spaces and then we want to use this locally convex approach structure (as we will call it) to create a canonical numerified counterpart of the classical topological projective tensor product, overlying the latter in a natural way. keywords: approach; convex; space; vector cache: agt-2031.pdf plain text: agt-2031.txt item: #283 of 431 id: agt-2032 author: Karapinar, Erdal; Tas, Kenan title: Quadruple fixed point theorems for nonlinear contractions on partial metric spaces date: 2014-04-01 words: 6019 flesch: 86 summary: x ∈ X, ε > 0}, where Bp(x, ε) = {y ∈ X : p(x, y) < [48] W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed mono- tone mappings in ordered partial metric spaces, Math. keywords: metric; point; spaces cache: agt-2032.pdf plain text: agt-2032.txt item: #284 of 431 id: agt-2033 author: Bartsch, René; Poppe, Harry title: A short note on hit-and-miss hyperspaces date: 2003-10-01 words: 4299 flesch: 81 summary: Then for each element x ∈ X, all refining ultrafilters of ϕ contain the complement of an open neighbourhood of x. the upper–Vietoris topology, there must exist finitely many P1, ...,Pn ∈ X with M ⊆ ⋃n j=1(O c Pj ) keywords: compact; i∈i cache: agt-2033.pdf plain text: agt-2033.txt item: #285 of 431 id: agt-2034 author: Preuss, Gerhard title: A better framework for first countable spaces date: 2003-10-01 words: 4785 flesch: 77 summary: 289–299 A better framework for first countable spaces Gerhard Preuß Dedicated to Professor S. Naimpally on the occasion of his 70th birthday. A better framework for first countable spaces 291 2) Let (X, W) be a uniform space. keywords: convergence; semiuniform; space cache: agt-2034.pdf plain text: agt-2034.txt item: #286 of 431 id: agt-2035 author: Bourhim, A. title: Bounded point evaluations for cyclic Hilbert space operators date: 2003-10-01 words: 6027 flesch: 81 summary: The local resolvent set of T at a vector y ∈ H, denoted by ρ T (y), is the union of all open subsets U of C for which y ∈ ranTU . For an operator T ∈ L(H), we denote as usual by σ(T) := {λ ∈ C : keywords: ba(t; cyclic; k(λ; operator cache: agt-2035.pdf plain text: agt-2035.txt item: #287 of 431 id: agt-2036 author: Artico, Giuliano; Malykhin, Viatcheslav I.; Marconi, Umberto title: Five different proofs of extraresolvability of countable totally bounded groups date: 2003-10-01 words: 3623 flesch: 77 summary: Let G = {gn : n ∈ ω} be a one to one numeration of a countably infinite group G. There exist infinite subsets Xn, n ∈ ω, such that the subsets Tn = {g1, . . Recall that a family D of infinite subsets of a set is said to be almost disjoint if A∩B is finite whenever A and B are distinct elements of D. Below we give a small survey with different proofs of extraresolvability for countably infinite spaces and, in particular, for totally bounded groups. keywords: disjoint; group; infinite; subset cache: agt-2036.pdf plain text: agt-2036.txt item: #288 of 431 id: agt-2037 author: Dikranjan, Dikran; Marconi, Umberto; Moresco, Roberto title: Groups with a small set of generators date: 2003-10-01 words: 12957 flesch: 80 summary: The class S of small generated groups. [21] J. Humphreys, Linear algebraic groups, Springer Verlag, New York–Heidelberg–Berlin, 1975 [22] V. Malykhin and R. Moresco, Small generated groups, Questions Answers Gen. Topology 19 (2001), no. 1, 47–53. keywords: generators; group; group g; infinite; lemma; microscopic; right; set; sets; small; subgroup cache: agt-2037.pdf plain text: agt-2037.txt item: #289 of 431 id: agt-2038 author: Holá, L'Ubica; Pelant, Jan; Zsilinszky, László title: Developable hyperspaces are metrizable date: 2003-10-01 words: 3985 flesch: 71 summary: Let y ∈ X be a point different from x. Let x ∈ X be such that for every U ∈B(x) and K ∈ K(X) there is some xU,K ∈ U\K (here B(x) stands for a base of neighborhoods of x). keywords: cl(x),τv; proof; proposition; space; topology cache: agt-2038.pdf plain text: agt-2038.txt item: #290 of 431 id: agt-2039 author: Di Caprio, Debora; Watson, Stephen title: Orderability and continuous selections for Wijsman and Vietoris hyperspaces date: 2003-10-01 words: 7684 flesch: 78 summary: <{(Un, 0 with d(a,b) < with d(x,y) < s + t, there exists z ∈ X such that d(x,z) < s and d(z,y) < keywords: metric; path; space; topology; wise cache: agt-2040.pdf plain text: agt-2040.txt item: #292 of 431 id: agt-2041 author: Dolecki, Szymon; Mynard, Frédéric title: Hyperconvergences date: 2003-10-01 words: 13440 flesch: 72 summary: I (M is coreflective if ξ ∈ M implies fξ ∈ M, and ∧ i∈I ξi ∈ M whenever ξi ∈ M for each i ∈ I). If J is a property of convergences, then by definition ξ ∈ J∗ keywords: compact; convergence; family; filter; hyperconvergence; set; sets; topology cache: agt-2041.pdf plain text: agt-2041.txt item: #293 of 431 id: agt-2042 author: Di Maio, Giuseppe; Meccariello, Enrico; Naimpally, Somashekhar title: Bombay hypertopologies date: 2003-10-01 words: 10221 flesch: 76 summary: ≤ σ(γ,γ0; ∆); (b) σ(γ,γ0; ∆) = σ(γ; ∆) = τ(∆); (c) for each B ∈ ∆ and W ∈ τ, W 6= X, with B ⊂ W , there exists a B′ ∈ ∆ such that B ⊂ B′ �γ W ; (d) whenever A ∈ CL(X), B ∈ ∆ and A∩B = ∅, then A6γB. Now, we compare two proximal hit-and-miss hypertopologies associated to the same cobase ∆. Theorem 3.12. The following are equivalent: (a) σ(γ1; ∆) ≤ σ(γ2; ∆); (b) for each B ∈ ∆ and W ∈ τ, W 6= X, with B �γ1 W , there exists a B′ ∈ ∆ such that B ⊂ B′ �γ2 W and γ1(B) ⊂ γ2(B′); (c) whenever A ∈ CL(X), B ∈ ∆ and A6γ1B, then there exists a B′ ∈ ∆ such that i) B ⊂ B′, A6γ2B′ and ii) whenever C is the range of a net satisfying C ⊂ (B′)c and Cγ1B then Cγ2B′. Corollary 3.13. keywords: space; topology cache: agt-2042.pdf plain text: agt-2042.txt item: #294 of 431 id: agt-2044 author: Di Maio, Giuseppe; Meccariello, Enrico; Naimpally, Somashekhar title: Graph topologies on closed multifunctions date: 2003-10-01 words: 9195 flesch: 84 summary: We say that Z is locally ∆ iff for each z ∈ Z with z ∈ V ∈ τ, there is D ∈ ∆ with z ∈ intD ⊂ D ⊂ V . In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X ×Y using various hy- pertopologies. keywords: compatible; space; topology cache: agt-2044.pdf plain text: agt-2044.txt item: #295 of 431 id: agt-2045 author: Georgiou, D. N.; Iliadis, Stavros; Papadopoulos, B. K. title: n-Tuple relations and topologies on function spaces date: 2003-10-01 words: 4126 flesch: 86 summary: We consider the map F : F × Y → Z such that F(i,y) = z1 for every y ∈ Y , and F(j,y) = z2 for every j ∈ F \{i} and y ∈ Y . ∈ U}, where y ∈ Y and U ∈O(Z), is a subbasis. keywords: c(y; topology cache: agt-2045.pdf plain text: agt-2045.txt item: #296 of 431 id: agt-2046 author: Lowen, R.; Sioen, M. title: A note on separation in AP date: 2003-10-01 words: 4918 flesch: 78 summary: The implication (1) ⇒(4) is proved using the implication (1) ⇒(3) because for all x ∈ X, δ(·,{x}) ∈ 478 R. Lowen and M. Sioen R. To prove the converse one, take x,y ∈ X, x 6= y and assume without loss of generality that γ(x) + ε, with A(ε) := {z ∈ X | δ(z,A) ≤ ε}. keywords: approach; spaces; |ap| cache: agt-2046.pdf plain text: agt-2046.txt item: #297 of 431 id: agt-2047 author: Iliadis, Stavros title: Some properties of the containing spaces and saturated classes of spaces date: 2003-10-01 words: 8916 flesch: 79 summary: We show that if T is a containing space constructed for an indexed collection S of spaces and for every X ∈ S, QX is a subset of X, then the corresponding containing space T|Q constructed for the indexed collection Q ≡{QX : X ∈ S} of spaces, under a simple condition, can be considered as a specific subset of T. We prove some “commutative” properties of these specific subsets. ∈ τ} : X ∈ S}, then the elements of BT are denoted by UTδ (H), δ ∈ τ keywords: restriction; t|q cache: agt-2047.pdf plain text: agt-2047.txt item: #298 of 431 id: agt-2048 author: Wilczynski, Wladyslaw title: Density topology and pointwise convergence date: 2003-10-01 words: 1688 flesch: 69 summary: The above observation was a starting point to study a category analogue of a density point, density topology and approximate continuity. Keywords: approximately continuous functions, I-approximately continuous functions, topology of pointwise convergence. keywords: density; topology cache: agt-2048.pdf plain text: agt-2048.txt item: #299 of 431 id: agt-2049 author: Mandal, Dhananjoy; Mukherjee, M. N. title: Near metrizability via a new approach date: 2014-04-01 words: 4180 flesch: 82 summary: As B is a pseudo-base for X, there exists B ∈ B such that x ∈ B ⊆ U. Since B is a pseudo-base for X, there exists U ∈ B keywords: base; pseudo cache: agt-2049.pdf plain text: agt-2049.txt item: #300 of 431 id: agt-2050 author: Alaste, Tomi Matias title: Function lattices and compactifications date: 2014-05-08 words: 10956 flesch: 84 summary: If F contains only the constant functions, then {X} is the only F-filter on X. On the other hand, if F = ℓ∞(X), then every filter ϕ on X is an F-filter on X. Let ϕ be an F-filter on X and suppose that A ∈ ϕ satisfies A 6= X. Pick some B ∈ ϕ and a function f ∈ F with f(B) = {0} and f(X \A) = {1}. Suppose also that there exists an F-filter ψ on X which properly contains ϕ. Pick some set A ∈ ψ \ ϕ. Pick some B ∈ ψ and a function f ∈ F with f(B) keywords: filter; let cache: agt-2050.pdf plain text: agt-2050.txt item: #301 of 431 id: agt-2057 author: Benkafadar, Nasreddine Mohamed; Gel'man, Boris Danielovich title: On some topological invariants for morphisms defined in homological spheres date: 2015-01-28 words: 5072 flesch: 78 summary: This finding offers the opportunity to get the morphism F ∈ MorT op(X × Thus, for a given object (X, A) ∈ Obj(T op(2)) and a mor- phism f ∈ MorT op(2) ((X, A), (Y, B)) the functor H assigns a graded group {Hi(X, A)}i≥0 and a homomorphism of degree zero {Hi(f)}i≥0 ∈ MorGd({Hi(X, A)}i≥0,{Hi(Y, B)}i≥0. 1.2. keywords: mort; multivalued cache: agt-2057.pdf plain text: agt-2057.txt item: #302 of 431 id: agt-2058 author: Shakhmatov, Dimitri; Tkachenko, Mikhail; Tkachuk, Vladimir V.; Wilson, Richard G. title: Strengthening connected Tychonoff topologies date: 2002-10-01 words: 39501 flesch: 82 summary: +>��� � � � #���� �K4 0R�Y+J��:��������lN � � �l+R0J��� i%k��x�xnUr�z?���Gw+zq{ �2Q�rDt S�� i w7lmk��utur � xg� ��E�j�� �j� �?���8F!��E(G*� � E����`� �`�����,a � tur �\nk� 4 � �l� � 4 ����� ��� �b'c� � � - � # +2��� ��� � �b�,+ ��- �&��� �$k�om~Uk���Q]rDt S��T�Gw+zq{ ���%y��u� ���RT � ��E�j�E ��� rDkD�D� � H(G�F������ � �?���� �����rDv�nU� � turDv �^~�� � �&� � �Y� �/+J��� �3 5 � {z� � � �gw7lmol]�wU��w � ��E(G�G*� � ����� � � U��(�(lmw7n/S �2=P�l�� 4 ��+2��� �3 'c-8� � 3����(!&+ ��� U rP� | k�p!k��uk�v7�xw7rDs | k�p!k��uk�v�tu~?w7�F�(�uv�nU�Dlmw ��| l�w7rDoq� w+zmtuk�r�o �*nUlmtunUo;� � S�k�� � � � ��E�j�� ��� pDp �7H����&FJH�j7�D���(�xnUlmtu~?w7r)�Gw+zq{DnU�w+zmtu~?w7� ��k*~Utunjz ���k ]y�omomt w7r)k�lqtuv�turFw7� turP�kU}]�S�nUoqzqt ��w� � w7s �F�(w7y � �D�D�J 1��n?l?�F�Gw+z?�PA2� � ��E7��� �j� �(GIE&FJH���H�� � �?����_D� �`�z�(y�zq{Dlqtun$w7rDse��� ������zqk�rDn � ��+ �(- �&�r:k02����� - � �L� � -�4 � � � % + �(� � ' � � �$+ ���&�8�&���I� - � �L� � -&4 � � �8! � ��� 4 ���R� yDr�s �!�Gw+zq{ �Lh C � ��E(GIH �j� E��8F!�?����� � ��H���_D� �`�>�(y�zq{Dlqtun � ��� ������zqk�rDn � w7rDs)� � ���R�gw7v�n � q1��%�'c#$� � - � �L� � -&4 � � � % + ��� � ' � � �$�lN 4 02�*��� � � ��� {�lqk*~��D���xnUl����Gw+zm{ �F�*k�~�� x>� � ��E(G7� ��� �?��E&F!��j���� � �U�I�����R��nj�]t zqz �>��+ ��� � � � # �lN[��� 4 � 4 02�8����� 4,'c-�4 ��+J��� �3 5 �>f y � n��Gw+zq{ �R_F�PA2C � ��E7�(H ��� H���E&FJH�H�H�� � �?���[U��L_�yD{��w7ol] ��? � � ��')� � �JN�! � -&4,' � � � 'c�w4 �/+J��� �3 5 � �Gw+zq{ �Fi nUr�zmlqn | l�w7~jzqo H7� � ��k�lWzm{V��k��u� w7rDs � �(�;� oqzqnUlmsFw7� ��E(G+�D� � ��j����(� ��� �*{Fw7p�tulmk&S*o � tut �7���t3�!2� � �K��+J� � ��� 4 � ��� �d4 02� - 0 � � �(-�4 �&� s � � � � 'c4O5d��� � :�� ' 3�0 4 'c����'c- � # � + �(-�4}� � f k � � �D�T�e�D���2 ��iAJh � ��E(G+� ��� ���&FJj���� � �&G&� f ���*{Dw � {D�w+zqk&S � � � |�� w7~�{DnUr � k � � � |�� w7~�{*y ��� ���7�gw+zmoqk�rRw7rDse b�i�Ktu�uoqk�r � u � 'c4 02��� � ��� 4 - ��! �L4}��� � � � �����?z� - 0J� - � # + � � 4 ���,+ �(- ��� � ��� #*�&%�'c#$� �r� 5(- 02� � �l� - � �L� � -&4 � � � {�lqk*~����(�xnUl?� �Gw+zm{��!�*k�~��iA2� x � ��E�E�� ��� �(GIE&F*���(G*� � �?���[{��+�*tu�xk�r ��� � � %���# + � ���N ��#*�&%�'c#$� � - � �L� � -&4 � �M��� !2� � ���c���,+ ��- ����� yDr�s �7�Gw+zq{ ��AJC>C � ��E(G7� �j� �?�(G�F!��j�H�� � ��E���_D� {�� | {�k��w7o � qZ�&%(')#*� � - � �L� � -&4 � �r4 �/+J��� �3 ' �&��� _D�F��yDoqzql�w7� ���Gw+zq{ ���*k�~�� h � ��E�j�� �j� G7���&F2G7����� � ����� � � |�� w7~�{�y �!�*�r02� �e� � - � �L� � -�4 � � �,+ �(- ���$0 � ��� �L'c- � - � �L� � -&4 � � + ��� ')#*� 3����(� { lmk�~����(�xnUl?� �Gw+zm{��!�*k�~��iA2� x � ��E�E�� ��� H7�(H(G�FJH7���(j�� ��������� � ��������� � � �� ��������N����� �� ��C �� � � �� a � a �����q��� yM��� � ���8����������� lQm,ozp8r2sMput[rwvuxqy � LNWoRTJ d p]LtY d U�� �:R d�� Ltp]R d�k�m�b � � R m #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: = �; aö �; aø �; d �; e �; ih �; j �; k �; klb �; mh �; rpn �; u �; ueyampqgf �; uty �; äaå �; å �; ækè �; çø �; è �; è4ä �; î �; ñ �; ò �; ø �; ù �; � 1å; � ^; � aå; � b; � dfb; � jtklb; � l; � ltj; � m; � qsl; � qø; � r; � v; � w; � y; � ä; � çö; � é; � ö; � ö@ù; � ú; � úwö; � þ; � � cache: agt-2058.pdf plain text: agt-2058.txt item: #303 of 431 id: agt-2059 author: Gusso, Riccardo title: Large and small sets with respect to homomorphisms and products of groups date: 2002-10-01 words: 17704 flesch: 32 summary: A E 5pvTn�L�/$ � F E ` W XVL_^%`Da�X `2/ A � F A E 5 7 I8(9(�*�5§ý\é Ø;à1ç Ù�ð2Ý4Ü Ü% � F E é à âÆÙ�ç Ü'Ý4Ø;Þ�ßeñ�õ �mØ;Ù�Û�Ð�ÏÆÐ ë�Ð ��ß@ç¶çAè�ß@âG� � N A � S,� E N A E ñ¨ß ��âÆé°çAßúà1Ú�ê èöç;è�ݬç A � \²ù& � � � � �²Ý�â�ã[A E \pù' E � � E �²Ý4Ø;ßUâÆÙ4ç Ü'Ý4Ø;Þ�ß�Ð�2ß=ç ñ¨ß ! #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: k �; l �; s �; sij �; t �; w �; y �; ß �; àaú �; á �; âæß �; âæù �; ã �; çaß �; çaè �; ñ �; ò �; ó �; ø �; øaù �; ù �; ú �; ý �; � =; � j; � jij; � n; � à1ß; � â; � ç; � ç;ý; � è; � é; � ê; � í; � øaþ; � ûæü; � ü; � ý4ç; � ý4ü; � � cache: agt-2059.pdf plain text: agt-2059.txt item: #304 of 431 id: agt-2060 author: Bosi, Gianni; Herden, Gerhard title: On the structure of completely useful topologies date: 2002-10-01 words: 63717 flesch: -195 summary: +/*.;_2�)�OM9�*.+06(O�� H ������� �X����� ����� [��:��� ���d[���� �� G�����3��� � �����Q� � � � � ��E�� � � � � �(�>� � � �g�������� �� �� � � �DH ���,���{� �U1�*.S�#���#K�<4&#&)RbN%&gRtM#&7�7 %V�{#&Od#&4&%(- +� (%:�&-,#��5��X ��� ����� ,���GY� �� Z�������� � �� �� ������ ��$� �� �� � ���� �Ul�� ��K� � ��� ������� � � � ����� �>� � � F:�>� � � ���������� W�� �� �N� XI��� � �K�+0#<1�%(Od��1(#Ug�%(4&%:�<-.#�15;>1&*�#<7�15� � ��� � � ���[���� ���������?���� ��� z ��� �� � � � � � � � �Q������j��� � � ��� � � � ����E�� � � � � F:F>�����M~ �$� ���&�PLM#<7�+09&6(O *.+,O�)D6()�1�)�*.+,- +=*,;�2�)�OM9�*.+06(O�1�+,O�*�6&gG6(-.65�>+09&%(-\1�g�%:9<#&15� � � Z>� �*���[��� H � ��� �X����� ����� ��� � �N[���� �� GJ�������� ����X� �b���g� ���:��� ��� ����� � � � ��� � ����� �&E����f� � � F:]>����� � �P� �(r ��� >�jLM#<7�+=§�9<6(OD*.+,OG)d6()�1�#5�:*0#&OG1<+06(O�6U2 % g�%(4|*,+0%(-�6(4&�:#&4&� � ������ ������� H � �%��� �X����� �����ckc���Kz ����X� ����� � ����� � � �)��� ��EQ� �R� � � Fpop����� � �{� �Kr ��� >���P�>+,1&*�#� � � �H ���,�%�:���P�>+,1�*0#&Od9&#R6U2�%(O 6(4&�:#<4|§,gG4&#&1|#&4&h(+,OG� 2�)�OM9�*.+06(O 6(O %�OM6(4<7 %(-,- ;£gG4&#&6(4&�:#<4�#<�$1UgG%:9&#&� ���� � ���%� ��� ����� � ��� �%����� � �� H ������� �X� ��� �����D[>�:��� ��� ���� � � � ��� � �����>�&E������ � � F:�>� � � �dH ���,���{�dLd6(7 #_��#+,1�*0#&Od9&#�6U2�6(4&�:#<4NgG4&#&1|#&4&h(+,OG�N2�)GOd9|*,+�6(OG1<� H ������z � �X����� �����D[��:��� ���d[{��� �� G��������� � � � ��� � � � � �|E���� � � � F{�K� � � �cH ���,���:��i 4&#<7 %(4<'�6(O�%�)�*.+,- #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: aa �; ac �; d �; d4 �; e �; fe �; fs �; j �; k �; l �; l2 �; n �; o �; q �; u �; v �; w �; y �; z �; ¦ �; � *3d4; � -s; � =; � >=; � c; � dt; � g; � gh; � r; � |; � û; � � cache: agt-2060.pdf plain text: agt-2060.txt item: #305 of 431 id: agt-2061 author: Schellekens, M.P. title: Extendible spaces date: 2002-10-01 words: 31598 flesch: 67 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. K�è�� �� �D ��G�E���E�(�D�H���!Uû���å�ð�ìpâ�ë=è�ì R O ã(Mqâ�ã�äAå�æF.%î�ä1è�â�ì¼ñ�æ�%#çfè@éAê;å ëaû å'ä�ì¼èDh{ðpè�ì R O û���.)>0;9 %X4�� �G)!�û*./)1029<%�0;û�.9*0;)*%$#G- % è�ì¼å ä;ë=â{äAä�ã ù è L è=ïpã�çfî�S�è�ä�ñ ù M�â{ã�äAå�æCî�äAè@â�ì¼ñ�æIç�è@éAê;å ë�ä1î{ã�ë=è�ä@ò _ keywords: d �; e �; k �; kpè �; l �; mqâ �; q �; r �; s �; y �; ã �; ä �; äaå �; å �; ç �; è �; è@å �; êañ �; ì �; îlñ �; ñ �; ù �; ú �; � $c; � =; � g; � j; � kqé;ã; � p; � w; � â; � ä1å; � äaè; � äaî; � æcç; � è@ê; � é; � é;k; � éaè; � éañ; � ébk; � ê; � êaè; � ë; � ë@è; � ìpå; � î{è; � ð; � ðpè; � ò; � � cache: agt-2061.pdf plain text: agt-2061.txt item: #306 of 431 id: agt-2062 author: Mendoza Iturralde, Pablo; Tkachuk, Vladimir V. title: Cofinitely and co-countably projective spaces date: 2002-10-01 words: 22170 flesch: 23 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. m� � d6� iA¦�§^n�¦�O 9|ü0'4�aó�ý=ü j � G�ð��)9;�)9|ü*$�')$�ó �Vþ�ï.�Üü�ïN�;þ��uþ�� þ�2�ôªð�'`ý=þ�#Cý@þ�$|ÿ��;ó�% � ô �|ï;þ �#ü�ý!�;ð��ü¼ó�ÿ��³ÿ�þ �Xý=þ�ÿ�ý=ü�ÿ��Aï ó(�Aü��³ó�ïAþ�$|ÿ��ªóK�aÿ|ð]�;ü '1üJ��+ , {�x�x��-*N�¸ó�ý:9xý@þ�ÿ��Að ÿ�$|þ�$A'cï;ü�ó��]#y�ó �-$|ü��n1�$|ÿ�ý!�;ðòþ�ÿ =Úþ�ÿ j � ð�'düJ�ü@ÿ��)$�ó���� ô�ý=þ�ÿ�'4�;ó4ÿ���� �.9�ó(��ð�'J�d�)9|ü�ïAü¶üJ_�ð�'4�.'�� � . keywords: = �; aó �; aü �; aþ �; cf �; j �; k �; uþ �; v3` �; |ï;þ �; ¢ �; ¦ �; ïaü �; ñ¶ó �; òü �; ó �; üü �; ý@ü �; ýj �; ÿ �; � '1ð; � '4; � )9; � +; � =; � x7\; � y; � ïaþ; � ðòÿ; � òô; � ô; � ø; � ü; � üð; � ý; � þ; � � cache: agt-2062.pdf plain text: agt-2062.txt item: #307 of 431 id: agt-2063 author: Smyth, M.B.; Webster, J. title: Finite approximation of stably compact spaces date: 2002-10-01 words: 65580 flesch: 29 summary: �W����*-�-& ������*�?=%+*+nO!#&���&(� ��*,����9;��*[üm��0�!,?=��*�Kgs1t�H4�#uSt��RH�t�H��]!-������%+!�þ %PJ�% 9;���(���ST_&('�Mh���$!#%+*-)S�S�,&(��' M�%+'�%�*�����&���%+!�� !#�,���-%+�Q%+' �<�X��?�% ���$��0=�e����������� �e��*�?=%�*,%+? !-������%+!`&�'��,J�%k��*,%+��%+?=&�'�MX!#%�� �,&(��' Z % /1� � � &%�!&%'�)(�&H7 � 7 �pH�zL2�Ua;�8k7.NJH5r � r0L�|U��u�t�� s1t�H4�#uSt��8H�t2H��X|Us�r832H $`-D56H�{fz!54H.|Us6H4� 3�w4r0/¥w� �r�z�w4u�{^u�t��RH�t5u0,az!54H L�s�s6H�tkziu�s�u�/(u21�O 3�u�wy{ 3�w'�RH�|Y[Rwyz!5 8 $ 5 t,u+u3,6$m �0����$� ! #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: !i �; %+! �; %+' �; %+*, �; %5 �; %p �; '$!8 �; *,%+ �; *,%+!-% �; *-9;%+ �; + �; -*,0 �; 1%+ �; = �; ?=& �; d �; e �; f �; h �; j �; k �; l �; m �; n �; o �; pj �; q �; q6 �; rh �; rr3jh �; s �; st �; t �; u �; v �; y �; z �; ¦ �; ø �; úh �; � !a; � '$; � '^; � *,%+; � +; � ?=; � b; � c; � g; � tut; � ua; � w; � w4u; � x; � |; � ú; � þ; � � cache: agt-2063.pdf plain text: agt-2063.txt item: #308 of 431 id: agt-2064 author: Richmond, Thomas A. title: A curious example involving ordered compactifications date: 2002-10-01 words: 18301 flesch: -2 summary: +1%!(�%'78%�<�,1$!*'7=3�(>*#$!!3?� � ��� � � � � � � � � � � �6@ACBED � � �0F�G � F��IHJ��F �� J0� �U�LK �NM[� �#� � ���NO)*'PC3' #%'�RQTS/%'&)(>*#$I+8, ./$!*0 � � � |�� � � ~A7V��? keywords: aü �; aÿ �; b �; bêú �; bêÿ �; bû;ÿ¥÷ �; d �; e �; j �; kj �; l �; u �; v �; y �; z �; êþ �; ë �; ù �; ùæú �; ú �; û �; � =; � g; � k; � n; � êú; � ø; � øaú; � ý; � ÿ; � � cache: agt-2064.pdf plain text: agt-2064.txt item: #309 of 431 id: agt-2106 author: Dimov, Georgi D.; Tironi, Gino title: Hausdorff compactifications and zero-one measures II date: 2002-04-01 words: 5452 flesch: 80 summary: A ∈ F}, where A ∈ C. Then the map ωC : X −→ ω(X,C), defined by the formula ωC(x) = {F ∈C : x ∈ F}, where x ∈ X, is a dense embedding of X in ω(X,C) and (ω(X,C),ωC) is a compactification of X equivalent to (max(B),ηB). For every Ū = (Ui,Uci)i∈ω ∈ L and every j ∈ ω, there exist k ∈ ω and V̄ = (V i,V ci)i∈ω,W̄ = (Wi,Wci)i∈ω ∈ L (which depend on the choice of Ū and j) such that Uc(j+1) keywords: space; sublattice cache: agt-2106.pdf plain text: agt-2106.txt item: #310 of 431 id: agt-2107 author: Alamar, Miguel; Estruch, Vicente D. title: A contribution to fuzzy subspaces date: 2002-04-01 words: 4886 flesch: 87 summary: Then, a fuzzy point xλ ∈ Y is a TY -adherence (cluster) point of A iff it is a T -adherence (cluster) point of A. 5. Then, λ + G(x) > Y (x) and thus xY (x)−λ ∼ ∈ G, and G 6⊂ Y − A since xλ is a TY -cluster point of A. Therefore, there exists x ∈ X such that G(x) > keywords: subspace cache: agt-2107.pdf plain text: agt-2107.txt item: #311 of 431 id: agt-2110 author: Zhuraev, T.F. title: On paracompact spaces and projectively inductively closed functors date: 2002-04-01 words: 4283 flesch: 77 summary: On paracompact spaces and projectively inductively closed functors 37 The class of stratifiable spaces was defined in 1961 by J.Ceder On paracompact spaces and projectively inductively closed functors 43 Proof of this theorem repeats the proof of Theorem 3.7 for stratifiable spaces. keywords: closed; functor; mapping; space; theorem cache: agt-2110.pdf plain text: agt-2110.txt item: #312 of 431 id: agt-2111 author: Naimpally, Somashekhar title: All hypertopologies are hit-and-miss date: 2002-04-01 words: 3867 flesch: 71 summary: Keywords: Hypertopology, Vietoris topology, Hausdorff metric, Hausdorff- Bourbaki uniformity, uniformity, proximal topology, hit-and-miss topology, lo- cally finite, Wijsman topology, proximal ball topology, ball topology, far-miss topology, Bounded Vietoris topology, Bounded proximal topology, Bounded Hausdorff topology, Attouch-Wets topology. More- over, Wijsman topologies are the building blocks of many other topologies e.g., (a) the metric proximal topology is the sup of all Wijsman topologies in- duced by uniformly equivalent metrics, and (b) the Vietoris topology is the sup of all Wijsman topologies induced by topologically equivalent metrics. keywords: finite; proximal; topology cache: agt-2111.pdf plain text: agt-2111.txt item: #313 of 431 id: agt-2112 author: McCluskey, Aisling E.; Watson, W. S. title: Minimal TUD spaces date: 2002-04-01 words: 4496 flesch: 79 summary: [16] H. Kawashima, On the topological product of minimal Hausdorff spaces, TRU Math. 1 (1965), 62–64. [18] S.M. Kim, Quasi-compact spaces and topological products of minimal Hausdorff spaces, Kyungpook Math. keywords: minimal cache: agt-2112.pdf plain text: agt-2112.txt item: #314 of 431 id: agt-2113 author: Heitzig, Jobst title: Every finite system of T1 uniformities comes from a single distance structure date: 2002-04-01 words: 5859 flesch: 85 summary: This implies that x,y ∈ ⋂ Vi and x,y ∈ ⋂ Vi′ for some i, i′ ∈ I, hence x = y = z. Then there is y ∈ X such that λ(y,s) > 0, σ(xy,ta−1,b) > 0, and σ(yz,ta−1,b) > 0. Proof. keywords: distance; quasi; set; λ(y cache: agt-2113.pdf plain text: agt-2113.txt item: #315 of 431 id: agt-2114 author: Arenas, F.G.; Puertas, M.L. title: Fenestrations induced by perfect tilings date: 2002-04-01 words: 3942 flesch: 78 summary: Keywords: Fenestration, tiling; grid, trace spaces, lower semicontinuous decomposition. Tilings. keywords: tiling cache: agt-2114.pdf plain text: agt-2114.txt item: #316 of 431 id: agt-2115 author: Fujita, Hiroshi; Shakhmatov, Dimitri title: Topological groups with dense compactly generated subgroups date: 2002-04-01 words: 1808 flesch: 70 summary: A topological group G is almost metrizable if there exist a non-empty com- pact set K ⊂ G and a sequence {Un}n∈ω of open subsets of G such that (1) K ⊂ Un for all n ∈ ω and (2) if O is an open set containing K, then there is an n ∈ ω such that K ⊂ Un ⊂ O. (Such a sequence {Un}n∈ω is called a neighborhood base of K in G.) It is well-known that σ-compact groups, separable groups and their dense subgroups are ℵ0-bounded ([2]). keywords: compact; group; open cache: agt-2115.pdf plain text: agt-2115.txt item: #317 of 431 id: agt-2116 author: Romaguera, Salvador; Schellekens, M.P. title: Duality and quasi-normability for complexity spaces date: 2002-04-01 words: 9597 flesch: 81 summary: Our basic references for quasi-metric spaces are [7] and [12]. This theory constitutes a part of the research in Theoretical Computer Science and Topology and is developed in the setting of the Smyth completion of quasi-metric spaces. keywords: bibanach; complexity; c∗f; d‖.‖c∗; metric; quasi; space; weightable cache: agt-2116.pdf plain text: agt-2116.txt item: #318 of 431 id: agt-2145 author: Mynard, Frédéric title: Coreflectively modified continuous duality applied to classical product theorems date: 2001-10-01 words: 66839 flesch: -66 summary: ÒPê@û�îAë ��û�ê@÷°N�Ø�Ô|Õ:Dxü�ûAë�ê@ûAö ÖcP8ô4õIì`înë�í|ñ'ì½ÿIûÜìªû�ìªí�înû�ì ��ê@ë�ö N Ù %|Õ�Dxü|ûAþ ë�ê<û�ö Ù1P�ô�õ�ì&��ê<ë�ö ô4õÄú õ�ï@ûAê@õ�ô4ñ|î üIô4ê ô�î>ï@ûAê@ú ��ô¨ï@ú�ë�õ�ë��8ÓbõFï<ë�ú�õ�ûbînë�õ���ûAê@ò�ûAõIînû�÷ ��ï@ü|ûbë�õ|û ë��Q�Yá�×�ë�í|ê@ì�ô4í�ìuN �cP2ë�ê���ê<ë�ö Dxü|û�ë�ê@ûAö Ñ|á�Ø �>á � õ�ì|ûAû�ì�ÕIÓbõFï@ë�ú õ|û�înë�õ���ûAê@ò�û�õ�înû�÷ ��ë�ê<ö ï@ü|ûqîAô4ê<ï<û�÷1ú'ô4õfînñ ë�÷<û�ì`ü�í|ñ�ñ2ë�� �Nô�õ�ì·ôYö½ô4ðfú'÷xð|ê@ë�ì|í�î>ï<þC÷1ï@ô�ÿ|ñ�ûÜú õmôY÷<í|ÿ:îAô4ï<ûAò�ë�ê@óÄë�� FIH_JMLÁú �µô�õ�ìmë�õ�ñ�ó³ú �°ú�ï ú'÷²ý�í�ë4ï<ú ûAõFïTú õ�ú�ï@÷²îAô�ê1ï@û�÷<ú ô�õfîAñ�ëF÷1û�ìfü�í|ñ�ñ�N Ù�%ªÕ�Dxü|û�ë�ê@ûAö Ù1PCá � õeîAë�õFï<ê ô�÷1ï�ÕFÚ�ë�ê<ë�ñ�ñ'ô4ê@óPѪá Ñ ��� ÷<ûAû�öÄ÷,ï<ë�ÿkûbë���ôÜõ|û � ï#óFðkûTô�õ�ì½ìªë�û�÷,õ�ë4ï���ë�ñ�ñ ë � ��ê@ë�ö ôYò�û�õ|ûAê ô4ñ:ê@û�÷<í|ñ�ï�ï@ü�ô¨ïbú õ���ë�ñ!��û�÷xînñ'ô�÷@÷1ú'îAô�ñ8îAô¨ï@ûAò�ë�ê@ú î�ô4ñkõ|ë4ï@ú�ë�õ�÷Aá Þ�á � }�� z|{ ~ ��� � � � � � }��2� � � � � z � ��� ����� �2}�� z wÁ�2� { � � �2��� � � z ww z � � z ~ � �rw��e} � ���|w � {�� ~ � � õ·ï<ü|û ���� � � � � � & d�.�.�� FT×�óeìªû $�õ|ú�ï<ú ë�õ °ð|ú � �� � � < �Tá õeï@ü|ûÜë4ï<ü�ûAê�ü�ô�õ�ì8Õ ��' w * < � ��' w * � ��ë�ê û#��ûAê@ó ' ô4õ�ì3��ë�êqû#��ûAê@ó * � ß�ú�õ * áe÷<ë³ï<ü�ô4ï � < µð|ú � �� � � á � õ�ìªû�û�ì8Õrú ��� 0 � 4|{ � � 2ñ ú�ö � >%z3A keywords: 73.1254vb �; d �; dfegb �; f �; k �; r �; tmë �; ¦ �; ¨ �; © �; ª �; ® �; ¶ö �; ß �; á �; ê@û �; ë �; ìªû �; ìªü �; í �; îaû �; ï �; ï@ü �; ðkë �; ò �; ó �; óeÿ �; ô �; õ �; öäð �; ø �; ù �; û �; ûaò �; ûaõfï �; ü �; � .1d; � .8d; � =; � ?.8`; � ?^; � b; � c; � dfe; � e84v,/^1; � g; � iû; � j; � n; � t; � w; � ©; � °; � ê; � ì; � í|ë; � î; � îaê; � îaë; � înë; � înï; � înû; � ð|ð|ñ; � ñ; � ô4í; � ô4ï; � ô4ñ; � ô4õ; � õfï; � ÷1ï; � ÷<ð; � ÷<÷; � ÷<ú¤ï@ú; � ÷@÷; � ú; � ú'îaô; � ûnï; � ÿ; � � cache: agt-2145.pdf plain text: agt-2145.txt item: #319 of 431 id: agt-2146 author: Balibrea, Francisco; Valverde Fajardo, Jose C. title: Topological normal forms of high degree for the simplest bifurcations date: 2001-10-01 words: 14735 flesch: -77 summary: Jé ÷�égî@éAí@òhâ ê�é�÷Rï<ç�âøî@ä4 �àøñ�Ó|ä�ê�÷ ï1ç�ß�ßJÞFï1â ê�á î � ä4îUç�ß�Þ�ê´ä4ß0Nß�à ñ�âøê�áUî � â ï�î@í@ä�ê�ï1ì�Þ�í@ò¨ä4î<â Þ�ê î � éÑé�æFç�ä4î<â Þ�ê Þ4ì � Ì�Õ Y � â ê î � éÑê�é � ãgÞ�Þ�í ÷�â ê�ä¸î@é�ï�ãAä4ê �éé2=�ß�í<é�ï<ï<é�÷ ä�ï � Ì�Õ � � � � j������ � j VXVUVB� ��� J ��� �� �� ������ � �������� ��� �� �� ��������� ��� é�ê � é �ä�à ä�ê�ãgé î � é�Ì�í@÷ Þ�í ÷�é�í�î@éAí@ò·ïAÓ � é � ä£è�é � � j � � � � � � j � � � w ó�ÞJÓ�é�è¸ä4à ç�ä¸î@âøê�á�î � â'ï]é�æ�çJä¸î<â Þ�ê·Þ�ê � Ð�ÓFÞ�ê�é � ä�ï ���!� Ð �� ���4� Ð �76 Яì�Þ�í�ä�ê�ñhã � Þ�â ãAéÞ�ì ����� Ð � Ó ��� ä4îlòhé�ä4ê�ï�î � ä¸î�î � é�Ì4í ÷ Þ�í ÷�éAí�î<é�í<ò·ï�ã�ä4ê ê�Þ4îl �é¯éAà âøò¨â ê�ä¸î@é�÷8Õ � Þ � Ó¸ß�í<Þ�ãgé�é�÷�â ê�áwâøêUî � é�ï@ä4ò¨é�ò¨ä�ê�ê�é�í � âøî � î � é¹Ò¸î � Þ�í ÷�éAí|î<é�í<ò·ï�Ó¸â°ì � é�ßJé�í1ì�Þ�í<ò î � é�ã � ä4ê�á�é � Ì�Õ Ô�Ð � � �kj ���2� � j�� � � � � éÑÞ4 �î ä4â êsÓ9 �ä4à'ä4êJãgâ ê�áhî � éUÒ¸î � Þ�í ÷�éAí¹î@éAí@ò¨ï�Ó � � j Ì � J ��� � �;j � � � � � � j Ì �������;j � � � � ��� ä4î�ß�í<Þ¸è�é�ï±î � ä4î � � � Ð �� � � � Ð � ä�ê�÷ î � éUÒ¸î � Þ�í ÷�éAí�î<é�í<ò·ï�ã�ä4ê ê�Þ4îl �éwé�àøâ ò¨âøêJä¸î<é�÷ì�Þ�ílä4ê�ñ¥ã � Þ�â'ãgéÑÞ�ì ��� ä�ê�÷ � � Õ3RÞ�í�!Fâ ê�á¨Þ�ê î � éQÎ�î � Þ�í@÷�é�í�î<éAí@ò·ïAÓ�âøì � é¯ò·ä/!�émî � é¯ê�Þ�ê�àøâ ê�é�ä4í¹î<í ä4êJï#ì�Þ�í<ò·ä¸î@âøÞ�ê � Ì�Õ Ô�Ô � � �-j����2� � j�� � � � j�� � � � � ì�Þ�í¹î � é�ï1éwî<é�í<ò·ï � é � ä£è�é � Ì�Õ Ô F � � � j Ì � J � � ����j Ì � � J� ���Bj Ò � � � � ���Bj � � � � � � j Ò ��� � � j Ì � J� ����j Ì � � ���Bj � � � w Ü � é�êsÓ�ä¸ì�î@éAílé�è¸ä4à ç�ä¸î@âøê�á¨Þ�ê � Ð�Ó � é¯ã � Þ�ÞFï1é ��� Ð ä4ê�÷ � � � Ð �� I � � � Ð �F � � � Ð � ��� ä4î�Ó2ä�ß�ß�à ñ�âøê�á î � é C òhß�àøâ'ãgâøîd��ç�êJã>î<â Þ�ê Ü � é�Þ�í@éAò î<Þ î � é·é�æFç�ä4î<â Þ�ê � Ì�Õ Ô F � Ó2ä�àøà Þ � ïç�ï�î@Þ·ò·ä/!�é � � � � �� ÐQì�Þ�ílï<ç'T¥ãgâ éAêFî<à ñ ï<ò¨ä�àøà t � t ÕC êZá�é�ê�éAí ä4àIÓ�â°ìqÞ�ê�é¯ß�éAí<ì�Þ�í@ò·ï�î � é�ã � ä�ê�á�é � Ì�Õ Ô�Ì � � �-j�� � � � j�� � � � j VXVUV j � J��xv � � J��xv � � �ä�à ä�ê�ãgâ ê�á¹î � é � F�� j Ô � î � î<é�í<ò·ï2ä�ê�÷ÑéAè¸ä�àøç�ä4î<â ê�álâ ê �K Ð�Ó£Þ�ê�é,Þ4 �î ä4â ê�ïY �ñwâøêJ÷�ç�ã>î@âøÞ�êä�ê é�æ�çJä¸î<â Þ�ê Þ4ì|î � éÑì�Þ�í<ò � F�� I M � ���4� Ð � � J���� � � Ð �� � J��xv � � Ð � I � J��qv � � Ð � j�� � VUVXVE��� � � F � ��� é�í<é � � VUVXV�� í<é�ß�í<é�ï1é�êFî@ïqäÑï1ç�ò¨ò·ä¸î@âøÞ�êQÞ�ì�î@éAí@ò¨ï ��� â ã � ä4í@é�ì�ç�ê�ã>î@âøÞ�ê¨Þ4ì�î � é !�ê�Þ � êãAÞFé�T¥ãgâ éAêFî@ï ���4� Ð ��� � � � Ð ���XwUwXw2� � J���� � � Ð � ä4ê�÷ ���4� Ð �C� � � � Ð �C�XwUwXw � � J�� � � � Ð �qw � �è�âøÞ�ç�ï<àøñ�Ó8î � â'ï¯à'ä�ï1î�é�æFç�ä4î<â Þ�ê ä4à àøÞ � ïÑç�ï¯î<ÞZò·ä/!�é � J��xv � � Ð � Ð � âøî � ä4ê´ä4ß�ß�í<Þ4Nß�í@â'ä¸î<éfã � Þ�â ãAéZÞ4ì � J�� � � � Ð � Ó�ì�Þ�í¥ä4à à ��� F�Õ �mï<â ê�á�ä4áFä4â ê`î � é C ò¨ß�àøâ'ãgâøî ��ç�ê�ã>î@âøÞ�êÜ � é�Þ�í@éAòZÓ � é � ä£è�é � J��qv � � � �� ÐQì�Þ�ílï1ç'T¥ãAâøé�ê�î@àøñ ï1ò·ä�àøà t � t ÕC êZá�é�ê�éAí ä4àIÓFì�Þ�ílä·ï<âøê�á�ç�à'ä4í@â°î#ñ·Þ�ì2î#ñ�ßJé �1Ó�â5Õ é�Õ Ó � Ì�Õ Ô�M � ���4� Ð �� � � � Ð �� VUVXV � J� � � � Ð �� Ð � �ç�î � J� �v � � Ð �76 Ð � î � é�ï<ä�ò¨éwß�í<Þ�ãgé�÷�ç�í@é ñ�â éAà'÷�ï � Ì�Õ Ô�Ò � ���4� Ð �� � � � Ð �� VUVXV � J� � � � Ð �� Ð � �ç�î � J� v � � Ð �� � J� v � � Ð �76 Ð ì�Þ�ílä4ê�ñ¥ã � Þ�â'ãgéÑÞ�ì|î � é�ãgÞ�é:T¥ãAâøé�ê�î ï ��� � � � �UwXwUw2� � J� v � Õ ������� � ��� �� ��+� � � ���� � � �� � ���� � ����� � ����� ��� � � ê î � é¯Þ�î � é�í � ä4êJ÷8Ó�ì�Þ�í � � �#Ó�ò·ä/!�â ê�áhî � é¯ê�Þ�ê�à âøê�é�ä4í�î<í ä4êJï#ì�Þ�í<ò·ä¸î@âøÞ�ê � Ì�Õ Ô�Y � � �-j����2� � j�� � � � j�� � � � j VXVXV j � J��xv � � J��xv � � � � � � ä�ê�÷ Jä4à'ä4ê�ãAâøê�áhî � é � F�� j Ô � î � Þ�í ÷�é�í�î@éAí@ò·ïAÓ � é � ä£è�é�Ó�ä¸ì�î<é�í�éAè¸ä4à ç�ä4î<â ê�á¨Þ�ê � Ð�Ó � Ì�Õ Ô£Î � � F � I M � � � J� v � � Ð � � J��xv � ��J� � Ð �� � J��qv � � Ð � I � J��xv � � Ð � j�� � VXVUV���� ��� ä4î2ò¨é�ä�ê�ï8î � ä¸î2é�è�é�í<ñmî<éAí@ò Þ4ì�Þ�í ÷�é�íBF � j Ô]á�í@é�ä4î<é�í:î � ä�ê F � j Ô,ãAä�ê Jé�éAà âøò¨â ê�ä¸î@é�÷8Ó é2=�ãAéAß�î�â ê î � é�ã�ä�ï<é � F �#Õ C êfï<ç�ã � ä¨ã�ä�ï<é�Ó � éÑã � ÞFÞFï1é � J� v � ÐQì�Þ�ílï<âøò¨ß�à â'ãgâøî#ñ�Õ �lê�ì�Þ�í<î<ç�ê�ä4î<é�àøñ�Ó�î � â ïmß�í@Þ�ãAé�÷�ç�í<é�÷�Þ�é�ïlê�Þ�î ä4ß�ß�àøñ âøêZî � éUã�ä�ï<é�ïlãAÞ�í@í<é�ï1ß�Þ�ê�÷�âøê�áhî@Þ ä�ê é�âøá�éAê�è¸ä4à ç�éÑé�æFç�ä4à'ïwÔ�Õ Ü � ç�ï�Ó � é � ä£è�é ß�í<Þ¸è�é�÷·î � éÑì�Þ�à à Þ � âøê�á¨í@é�ï<ç�àøî�Õ <>=@? #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: j �; t �; y �; ß �; á �; âøê �; ä �; ç �; é �; ê �; ì �; î �; ñ �; ó �; ù �; � àøà; � â; � âøî; � ä£è; � æfç; � éaê; � í; � õ; � ü; � þ; � � cache: agt-2146.pdf plain text: agt-2146.txt item: #320 of 431 id: agt-2147 author: Kennedy, Judy A.; Kopperman, Ralph D.; Wilson, Richard G. title: The chainable continua are the spaces approximated by finite COTS date: 2001-10-01 words: 22632 flesch: -3 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. F�,\N�� � F � m �~ x � ~ keywords: 6v8+c �; = �; @8 �; ab698+c �; e �; f �; fj. �; ipr �; j �; k �; kgf �; l �; q �; r �; rb?=����*�*¦*:%�*:.>?\&@�:.�<;*¦A3 2 ��� mKE ><;0¥�¤.: � ��;<� �j¦��E�*�#�4b ���*�I� 2 �P�p�*�rb ���#� �t���i�P� ���P�*�7¢T�P�*� 2 ¦.31�t 0�t�&��� +O#���#.V #�e?���$�.Vy���?�7 #&�?����+M#Ug.� e?��+M�.V +M#��%#.V #$e.j.�!���7�t��¦�3q�����!¦!31���0���*�   B �98 �&:.: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. keywords: c �; e �; f �; g �; ixo �; q �; t �; ¦ �; á �; ç �; èò �; ò �; òað �; óað �; óxò �; ü �; üjò �; ý �; � j; � jý=; � mpc; � n; � ñ; � ñ8ç; � óp; � ö*óx÷; � ÷/; � ø; � üæò; � � cache: agt-2148.pdf plain text: agt-2148.txt item: #322 of 431 id: agt-2149 author: Arenas, F.G.; Sánchez Granero, M.A. title: Directed GF-spaces date: 2001-10-01 words: 25807 flesch: -109 summary: Ø4æ�ç³õ1ø�öpö_åFõ1ãmñ@û�Ø�ñfñ<û�ãAÕ@ã�ã/��Ö'õ1ñ@õ � � � ��| �H� �]Q�ý¨Ö ×� � N�� �iT�G�Q V õ<ø�ä û�ñ<û�Ø4ñ � � �@| �!�}� � � � �@I ��÷Iå�ÕSØ4ý ý:GiQ ê�â�Ö¨æ_äPã]\[Ö õWû�Ø4ý¨÷zäAå�×�öpý ãPñ@ã�Þ���Ù � ãA×�×§Ø Úpê¨Ý¡ñ@ûpãAÕ@ãWã_�JÖ'õ#ñ õ | Qv\ õ<ø�ä û�ñ<û_Ø�ñ�� � ��| �2� � � � �@| �!�}� � � � �@I �PÞ�Ø�æ�ç�ûpã�æ�äPã��¸ãWû_صÿ�ã ñ@û�Ø�ñ I Qih � ��| �W÷Iå�Õ�ã�Ø�ä û~G Q Þ:Ø�æ�ç�õ<Ö¨æ_äPãe\ Ö õ� � Þ:Ö¨ñ 68¥�3 £�?�5�?$#�� <=¥�£�� 7 �B%(;=¥�£�?Æ¢�;=3=?'�&7 6)(n?@5+* � 143 #���68£��= @?'(�?�5/7>� ¤c7�£���5�£�A � ãAñ \ �~ãcØcñ@å�ö~å�ý å ��Ö'äAØ�ý~õ<ö�Ø�äPã Ø�æ�çYX �~ãfØsñ<Õ Ø4æ_õ1Ö¨ñ<Ö ÿ�ã���Ø�õ<ãSå�÷5�Fø�Ø�õ<Ö�ôCøpæpÖ¨÷Iå�Õ@×�Ö�ñ#Ùm÷Iå�Õ2\¦ê ó�å�Õsã�Ø�ä û h Q�X Þ ��ã�çJãAþ�æpãv��� K N8h]� ��I �YT I Q�\iV�ê�ü®ãiæpå4ñ@ã�ñ<û_Ø�ñe��� Ö õmØ ö�Ø�Õ1ñ@Ö�ñ@Ö¨å�æ�å�÷ \ ÷Iå�Õ�ã�Ø�ä û~hpQ^Zmê ¡ûpãf÷Iå�ý¨ý å���Ö¨æ!�mõ1ñ@Ø4ñ<ãA×�ã�æ�ñ õWäAØ�æ �~ãcöpÕ@å�ÿ�ã�ç�ý Ö( �ã ñ@ûpã�õ<øpÖ�ñ ØT�pý ãcå�æ�ã�õ¡Ö æ � �-�Cê ü®ã�çJãPþ�æ�ã�� � T-\ � � � ��Ù�� � ��I �BKRh]� �@I �PÞ���Ö�ñ@ûiñ<ûpãfå�Õ çJã�Õ�� � ��I �}� � � � �@| � Ö¨÷zØ�æ�çiå�æpý Ù�Ö¨÷ | QÂh �@I �>ê�ópå�Õ_h J k�Q[X0��Ö¨ñ<ûÂk r�hmÞ!�¸ã�çJãAþ�æpã�� C�� T�� C � � � ��Ù�� C�� � � C �@I �N�cK�� � �@I �>ê ¡ûpã�æ�� � Ø4æ�ç�� C � Ø4Õ@ã äPå�æFñ<Ö æFø�å�ø�õº×�Ø�öpöpÖ æ���õ¸÷Iå�Õ¸ã�Ø�ä û[hpQ+XwØ�æ�ç§ã�Ø�ä ûvk�Q[X ��Ö¨ñ<û~k�r�hmÞpØ4æ�ç��eK � � � � � ��� Ö'õ�Ø4æbãA×9�_ã�çpçJÖ æ��m÷IÕ<å�× \[Ö¨æFñ@åmý Ö ×��� N�� � T�h Q[X�V� ��ûpÖ ä ûiÖ'õ¡ñ<ûpãcÖ æ�ÿ�ã�Õ@õ<ã ý Ö ×mÖ¨ñWå4÷,Ø�çJÖ Õ<ã�ä>ñ<ã�çbõ1ÙJõ1ñ<ãA× keywords: @i �; j �; k �; pê �; q �; t �; © �; ® �; ± �; ³ �; ãpñ �; äaã �; äaå �; äpå �; å �; ç �; õ �; õ@ø �; ø �; ù �; ûpã �; � g; � n; � ª; � ®; � ×; � ã; � äpã; � äpñ; � æ; � æpö; � æpý; � çjö; � ê; � ñ; � ö; � ÷iå; � ø4ñ; � ø4ý; � ý; � ÿ; � � cache: agt-2149.pdf plain text: agt-2149.txt item: #323 of 431 id: agt-2150 author: Gutev, Valentin; Nogura, Tsugunori title: Selections and order-like relations date: 2001-10-01 words: 26852 flesch: -198 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. ô�à¤ò�?�òAà@ä�* � � � � � �G ï��@énë�ã4õ�ö8ë+��ä ! keywords: cò �; cô �; f �; g �; iá6 �; j_p;p �; l �; nò �; oòaõ �; q �; u �; v �; z �; ã �; ä �; ñ �; ò �; ó �; óaô �; ô �; ôd( �; õ �; õnò �; ù �; � j; � p; � w; � |; � à; � á; � â; � óaò; � óeò; � óeô; � õnô; � � cache: agt-2150.pdf plain text: agt-2150.txt item: #324 of 431 id: agt-2151 author: Chasco, M. J.; Martin-Peinador, E. title: On strongly reflexive topological groups date: 2001-10-01 words: 18319 flesch: -42 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. +,� +- s~ � � <�� +�nJC]� ü ÷��aø�� �9 B���Y÷p÷@õ¿÷���ü?�c÷<õ� Ôõ�ÿ õ�û�ù�� � � <�� +�noC�ü?�Rúk�Aõ��� �ÿ��Y÷��l��� �ú�ø@ú���ÿ��J���Y÷<ø@ü���ú���ÿ���÷<õ� �õ� ÿ õ�û�ü���ú4ÿ2ë5����ÿ ü'ú4öjû�ø<õ�þ� �ú4ö�ý_÷����1�!��ú4ø ú��>÷��Aø!��ý#��0�ö���ý���ù.�w6���<���C +/��~0�\����� �ú�ø@ú4÷�� ÷����` �õ�ü ö~÷!�²õ�/ � � <1� +�noCD% 0l����û�ø<õ�þ� �«÷���þ �Àü ö~÷<ø@õ�ý�þ ����ý ú4ø��=�Yÿ õ����Aÿ ù ø��Aÿ'ú¨÷���ýh÷<õ{÷����ca²ú4ö�ú��!� �9 �ú���� � � � � p 3 � 32� %ZM*öS/%ú��>÷��²÷����Aùwú4ø��V÷<õ� �õ�ÿ õ�û�ü?�Aú4ÿ ÿ ù{ü��<õ��«õ�ø� ���ü?�Î÷<õT2~þ�õ�÷<ü��Aö~÷Àû�ø@õ�þ � õ�/�÷����6�Yõ�ø<ø����� �õ�ö�ýHü ö�ûL�9 �ú���� � %6]�õ�øi�Aõ�ö �<ü'ý#�Aø¢÷����6��õ��aõ��«õ�ø� ���ü?�9� C e P3� 6 n�� ý#� 0�ö���ý@��ù CX<�jBC <���Con ���# ¿é54��KjO<���C�� jB~ P3� +��c~6�J% � ÿ���ú4ø@ÿ ù9C ü?���1þ�ø�:;� �>÷<ü����Ìú�ö�ý �Aõ�ö~÷<ü ö�þ�õ�þ �\4�ü ÷���7�&98 C n�:;����÷�����ø�� / õ�ø��¿÷����N2~þ�õ4÷@ü���ö�÷A��õ��«õ��«õ�ø� ���ü?��� ! keywords: = �; aõ �; aö �; aø �; aú �; d �; e �; k �; yõ �; z �; ôõ �; õ �; ö �; öq �; ø@õ �; ú �; ý �; þ �; � aÿ; � b; � g; � ø; � ü; � ýhü; � ÿ; � � cache: agt-2151.pdf plain text: agt-2151.txt item: #325 of 431 id: agt-2152 author: Torres Falcón, Yolanda title: Unions of chains of subgroups of a topologucal group date: 2001-10-01 words: 16995 flesch: -56 summary: #%$'&'� ( )*(,+�-*. � /10 � � � � )2( �34)*. � ����� P Ô æ¤ù<ø�ä úPÖT �Ö­×|ð@ú�Ö§ð�ð@úÐãL�îå�õ õ å �ÔöæÐ÷�äAå�æ�çIÔöð<Ô å�æ�ù�Ö4Ó@ãªù@Ö§ð@Ô ù:+�ã�ç � J ÔRQ�� ÿ Ô ù�ÖdæÐå�æ,bHã�Õ|ôIð#×¥ù<øÐò�ù<ãlð�å��[� 7 Ö4æ�çO; � ÿ ; >�� Ü J ÔöÔRQ ����� ÿ ���^Ö�æ�çO; ����� ÿ ; >v���îå�Ó�ã'��ãAÓ@×��T��� ÿ Ü J Ô ÔöÔRQ�� <��iÿ¤Ô��S�O>f�¶Ü J Ô��cQ<�îå�Ó�ã0��ãAÓ@× �T���E tá � ��� < � ��� ÿ¤Ô%���6>��¶Ü J �cQ<�îå�Ó�ã0��ãAÓ@× �T���E tá � ��� ÿ�� � ��� �û � ��� ¤Ô%��� >��¶ê BiÔ�&*� �¥�d7£Ö�æ�ç¿ù<øÐôÐô}å�ù<ã�� Ö�æ�ç�þ� ��� � ����� � � ! keywords: j �; © �; á �; ã �; äaå �; älå �; å �; ç �; ñ �; ó@å �; ö �; ø �; øðæ �; ù �; ù1ã �; ú �; úðã �; úðå �; � k; � ä; � æ; � çiã; � ê; � îå; � ð@ö; � ò; � ó; � ô; � õ|å; � ö4ð; � ö4ó; � ö4õ; � øðô; � ÿ; � � cache: agt-2152.pdf plain text: agt-2152.txt item: #326 of 431 id: agt-2153 author: Dikranjan, Dikran title: Continuous maps in the Bohr Topology date: 2001-10-01 words: 70971 flesch: -7 summary: � ' �Iü�� þ�þ= 4 � � � � �>4 � � � � ��4 � ��� � ��ûKA � KG:oI �s� > �^�� �ù�,���÷-')&c'4&3 �þ�KMa£ù4ö@÷'ù�T3,] (S=V3�� '<÷]����0e'@ù5-� �ùj*�ù�ö2'@÷�'@÷-���nù����©ùj�3 b'���Ss'#ú *9 ����Y� > &3 b� ( / � � � � � � 1 { ûc0)*3, ÷�'G0�÷-� ( / � � � � � � 1 � 3 4 � � ��� �=!\ -;4 � � � � � $�|6 - 3 4 � � � � �/�$ -;4 � ��� � � &5G6 � 0)��')&�ù�'\4 � � ��� �=!\ -�4 ��� � � �.$�e{ û�ù����54 � � ��� � �$ -a4 � ��� � � &5�{ û���#�úa[O, ù�÷ ø ��� 8n')&� b��� a� �ö).�÷-�3.u�3 '�4 � � � � �)!? �-<4 ��� � � �.$� -;4 � � � � � �$ -;4 � � � � �/&5+A #�ú > &3 ���ö4 Aø �3� ��ÿ A �=! ���_��$��2&5O{ ûX.�÷]a� �0bz �5ù��4 � ��� � �=! ���_��$��2&5�{ û×ÿ3 b����0) 9D�V3 ���'), ú1�O j ���� ,]V��� �4 ��� ��� �=! ���7�%$T��&5 ��ûX���ùu'@ù4÷],���S<')&� j�3 '���01÷]�� �'4&×÷0²÷]0�ùX�3 b'7��÷�'4&5*�ù4÷ ö)��÷0) _�J÷0�,���÷]��'B0)V3*3*9��ö)'40�ÿ3 YS�� >� �øOø©ù��3� þ��sY� �PTn14 � ��� � ��ûnù�0�ùc ����0�' ù���'\�3 'B b��� a� �ö).�÷-��.�')�Tû�� �� 9 � / � � � � � � 1 { û�ÿ�! / � � � � � � 1 { ûnù�����( / � � � � � � 1 { û3� 7â÷-')&g�%ùs�ù������=T�%�O �&�ù~a� �Iü�� e� 4 ��� ��� �>4 ��� ��� �âûKA 1B��� �% � b����0<÷�� Aö\02') b*5T�úl02') �*`'4&3 � ����0) 9D�V3 b�+ �0(��S<'4&3 �')&×ö4 b j, ÷ øO÷-'40ÊûV÷]�'�P =Y� ü3� �+� þ�� � KG:oIP)Y�Q� / � � � � � � 1 { ûn��÷�'4& ! keywords: '@÷- �; *9 �; + �; ab �; aö �; aù �; ba �; bd �; bh �; bw �; d �; d)a �; e �; ega �; hca �; iü �; j �; k �; kq �; lf �; n �; nù �; o �; p �; q �; s �; t �; u �; v �; wc �; wv �; y �; yk �; ys �; z �; © �; ªy �; ® �; ×÷]0 �; éù �; ö �; ög �; ø �; øc �; ù �; ú �; � '4; � '4&3; � '4v×ö; � '<÷; � '@÷-; � =; � \&3; � aba; � abab; � aö4; � aö@ú; � b; � c; � dmi3c; � fw; � g; � h; � jl; � j÷"0; � l; � lpe; � lpj; � m; � neq; � o3; � psr; � qy<; � t3; � t9; � v3; � w; � ©; � ®; � ö4; � ö@ù; � øx; � ü3; � ÿ; � � cache: agt-2153.pdf plain text: agt-2153.txt item: #327 of 431 id: agt-2230 author: Ursul, Mihail; Tripe, Adela title: Radicals in the class of compact right topological rings date: 2014-09-09 words: 2280 flesch: 80 summary: Every simple left Noetherian compact right topological ring R with identity of prime characteristic is finite. Proof. 15, no. 2 230 Radicals in the class of compact right topological rings of continuous endomorphisms of R (+) with the compact-open topology. keywords: ring; ρ(r cache: agt-2230.pdf plain text: agt-2230.txt item: #328 of 431 id: agt-2250 author: Milani, Vida; Mansourbeigi, Seyed M.H.; Finizadeh, Hossein title: Algebraic and topological structures on rational tangles date: 2017-04-03 words: 3983 flesch: 79 summary: Gen. Topol. 18, no. 1 (2017), 1-11 doi:10.4995/agt.2017.2250 c© AGT, UPV, 2017 Algebraic and topological structures on rational tangles Vida Milani a, Seyed M. H. Mansourbeigi b and Hossein Finizadeh c a Department of Mathematics and Statistics, Utah State University, Logan Utah, USA (vida milani@yahoo.com) b Department of Computer Science, Utah State University, Logan Utah, USA (smansourbeigi@aggiemail.usu.edu) c Department of Mathematics, Shahid Beheshti University, Tehran, Iran (hfinizadeh@gmail.com) Communicated by M. Sanchis Abstract In this paper we present the construction of a group Hopf algebra on the class of rational tangles. keywords: a1,a2; rational; tangles cache: agt-2250.pdf plain text: agt-2250.txt item: #329 of 431 id: agt-2281 author: Li, Ji; Peters, T. J.; Jordan, K. E. title: Computational topology for approximations of knots date: 2014-10-01 words: 6881 flesch: 77 summary: [12] J. Li, T. J. Peters, D. Marsh and K. E. Jordan,Computational topology counterexamples with 3D visualization of Bézier curves, Applied General Topology 13, no. 2 (2012), 115–134 [13] J. Li, T. J. Peters and J. A. Roulier, Isotopic equivalence from Bézier curve subdivision, preprint [14] L. Lin and C. Yap, Adaptive isotopic approximation of nonsingular curves: the parame- terizability and nonlocal isotopy approach, Discrete & Computational Geometry 45, no. 4 (2011), 760–795 c© AGT, UPV, 2014 Appl. High degree Bézier curves are often used as smooth representations, where computational efficiency is a practical concern. keywords: curve; lemma; point cache: agt-2281.pdf plain text: agt-2281.txt item: #330 of 431 id: agt-2305 author: Chaipunya, Parin; Kumam, Poom title: Nonself KKM Maps and Corresponding Theorems in Hadamard Manifolds date: 2015-01-28 words: 3398 flesch: 77 summary: Such point z∗ is independent of y ∈ M, so we prefer writing 1The quantifier ‘for some’ is used in some texts. ∈ A × B such that d(x, ȳ) = d(x̄,y) = dist(A,B), where dist(A,B) := inf{d(x,y),x ∈ A,y ∈ B}. keywords: kkm; point cache: agt-2305.pdf plain text: agt-2305.txt item: #331 of 431 id: agt-2815 author: Singh, S.L.; Kamal, Raj; Chugh, Renu; Mishra, Swami Nath title: New common fixed point theorems for multivalued maps date: 2014-05-23 words: 3115 flesch: 90 summary: Since Sx ∈ Px and T y ∈ Qy, d(x, Sx) ≤ ρ(x, Px) and d(y, T y) For x, y ∈ X, we follow the following notation, where S and T are maps to be defined specifically in a particular context: M(Sx, T y) = { d(x, y), d(x, Sx) + d(y, T y) 2 , d(x, T y) keywords: t y cache: agt-2815.pdf plain text: agt-2815.txt item: #332 of 431 id: agt-3010 author: Cánovas, José S. title: On topological sequence entropy of circle maps date: 2001-04-01 words: 2275 flesch: 80 summary: Universidad Polit�ecnica de Cartagena.[5] G. L. Forti, L. Paganoni and J. Sm��tal, Strange triangular maps of the square, Bull. N. Franzov�a and J. Sm��tal, Positive sequence topological entropy characterizes chaotic maps,Proc. keywords: entropy; maps cache: agt-3010.pdf plain text: agt-3010.txt item: #333 of 431 id: agt-3011 author: Rodríguez-López, Jesús title: Fell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence date: 2001-04-01 words: 9122 flesch: 79 summary: It is easy to show that d(x; �)�1(�1;�) = Bd(x;�)� so we obtain thatF�P = T �(Wd) on P0(X): In a similar way, it can be proved F�Q = T �(Wd�1)on P0(X):Now, we show that F+P � T +(Wd) on CLQ0 (X). We say that (X;P;Q) is pairwise locally compact if P is locally compact withrespect to Q and Q is locally compact with respect to P. 24 J. Rodr��guez-L�opezThis de�nition is not suitable here. keywords: double; quasi; space cache: agt-3011.pdf plain text: agt-3011.txt item: #334 of 431 id: agt-3012 author: Bosi, Gianni; Isler, Romano title: Continuous representability of complete preorders on the space of upper-continuous capacities date: 2001-04-01 words: 1660 flesch: 49 summary: In order to prove that u is upper semicontinuous (i.e., theset fx 2 X : � � u(x)g is closed for every real number �), consider any realnumber �, any point x 2 X, and any sequence fxng � X converging to x suchthat � � u(xn) for every n. Since the sequence fpxng � D converges to px 2 D,U is upper semicontinuous, and from the de�nition of U we have � � U(pxn)for every n, it must be � � U(px) = u(x), and therefore the conclusion follows. The following corollary to the previoustheorem concerns the representability of �X by means of a continuous or atleast upper semicontinuous utility function u on (X;d).Corollary 3.2. keywords: complete; preorder cache: agt-3012.pdf plain text: agt-3012.txt item: #335 of 431 id: agt-3014 author: Vidal, Anna title: Common fixed point theorems for a countable family of fuzzy mappings date: 2001-04-01 words: 3094 flesch: 88 summary: Let x01 2 X: Let (xrs) be the sequence in the proof of theorem 3.2.Now, d(x11;x12) � D(F1(x01);F2(x11)) and using one of the two boundaryconditions for D, it is proved thatd(x11;x12) � k1 � hd(x01;x11) and d(x12;x21) � k1 � hd(x11;x12):Similarly we haved(x21;x31) � k1 � hd(x12;x21);d(x32;x31) � k1 � hd(x21;x31); : : : :Let y0 = x01. By the above relations, one can verifythat d(yn;yn+1) < �d(yn�1;yn) < �n d(y0;y1) n = 1;2; ::: and for m > n itis easy to see that d(yn;ym) � �n1��d(y0;y1). keywords: quasi cache: agt-3014.pdf plain text: agt-3014.txt item: #336 of 431 id: agt-3015 author: Balibrea, Francisco; Cánovas, José S.; Linero, A. title: New results on topological dynamics of antitriangular maps date: 2001-04-01 words: 4545 flesch: 83 summary: [f1g, then � � # 2 Zn+m (where n +1 means 1)will denote the sequence � de�ned by �i = �i if 1 � i � n and �i = #i�n for anyi > �Now we �x X = I. It was proved in [3] that the inclusion (d) of Theorem2.2 can be strict, that is, there is an antitriangular map F holding(2.7) R(F) $ R(g � f) � R(f � g):We are able to give an example showing that(2.8) UR(F) $ UR(g � f) � UR(f � g);that is, the inclusion (c) of Theorem 2.2 can be strict. keywords: antitriangular; maps; p(f cache: agt-3015.pdf plain text: agt-3015.txt item: #337 of 431 id: agt-3016 author: Sapena Piera, Almanzor title: A contribution to the study of fuzzy metric spaces date: 2001-04-01 words: 4470 flesch: 78 summary: Therefore M(x;ai; t) > 1 � r and M(y;aj; t) > 1 � r. Now,M(x;y;3t) � M(x;ai; t) � M(ai;aj; t) � M(aj;y;t)� (1 � r) � � � (1 � r)> 1 � sfor some s 2]0;1[ by the assumption on �, and so M is F-bounded �Problem 3.10. Indeed, if (x;y);(y;z) 2 Un thenM(x;z; 1n) � min�M(x;y; 1n);M(y;z; 1n)�> 1 � 1n;and thus (x;z) 2 Un, i.e., Un � Un � Un. keywords: metric; space cache: agt-3016.pdf plain text: agt-3016.txt item: #338 of 431 id: agt-3018 author: Sánchez Granero, M.A. title: Weak completeness of the Bourbaki quasi-uniformity date: 2001-04-01 words: 6239 flesch: 86 summary: Then the net fF�;U :(�;U) 2 D � Ug (where (�;U) � (�0;U 0) if and only if � � �0 andU 0 � U) is clearly (U�)H-Cauchy and T (UH)-convergent to C. ThenC 2 C0(X) \ C�(F0(X)) Since C�0 2 K�0(X)there exists a �nite subset B of C�0 such that C�0 � V �(B) and henceF�0 � V �(C�0) � V � �V �(B) � U�(B). keywords: quasi; uniform; x;u cache: agt-3018.pdf plain text: agt-3018.txt item: #339 of 431 id: agt-3020 author: Császár, Ákos title: Merotopies associated with quasi-uniformities date: 2000-10-01 words: 5951 flesch: 82 summary: Then cU isa cover on X and, both U and U 0 being entourages on X with U � U 0, clearlyU(x) � U 0(x) for x 2 X so that cU < cU0. � U is point-symmetric. keywords: quasi; semi; symmetric; uniformity cache: agt-3020.pdf plain text: agt-3020.txt item: #340 of 431 id: agt-3021 author: Arhangelskii, A. V. title: An operation on topological spaces date: 2000-10-01 words: 7430 flesch: 69 summary: If X is a continuously diagonalizable Tychono� space with thecountable Souslin number, then every G�-dense subspace Y of X is C-embeddedin X. 26 A.V. Arhangel0ski��Proof. A central role in what follows also belongs 14 A.V. Arhangel0ski��to the notion of a Moscow space, which was recently shown to have delicateapplications in topological algebra. keywords: countable; diagonalizable; feg; point; space; theorem cache: agt-3021.pdf plain text: agt-3021.txt item: #341 of 431 id: agt-3022 author: Hernández, Constancio; Robbie, D.; Tkachenko, Mikhail title: Some properties of o-bounded and strictly o-bounded groups date: 2000-10-01 words: 7879 flesch: 83 summary: We can also as-sume that K1 � K2 � ��� � Kn � ��� . If � is non-limit, say � = � + 1, then we putG� = G� � Z � Z� � Z = Z�. keywords: countable; group; group g; � � cache: agt-3022.pdf plain text: agt-3022.txt item: #342 of 431 id: agt-3023 author: Ohta, Haruto title: Extension properties and the Niemytzki plane date: 2000-10-01 words: 8884 flesch: 83 summary: Then h � � is a continuous extension off over T � �E(T), where � : T � �E(T) ! [R in Example 2.3 by declaringthe sets fpAg [ (A n f1;2; � � � ;ng), n 2 N, to be basic neighborhoods of pAfor each A 2 R. The resulting space is �rst countable and is usually called a -space (see [4, 5I, p.79]). keywords: set; space; subset cache: agt-3023.pdf plain text: agt-3023.txt item: #343 of 431 id: agt-3024 author: Herden, G.; Pallack, A. title: Useful topologies and separable systems date: 2000-10-01 words: 10911 flesch: 68 summary: [0; +1[ that satis�es for all points x;y;z 2 X the following conditions.(PM1): �(x;x) = 0,(PM2): �(x;y) = �(y;x),(PM3): �(x;z) � �(x;y) + �(y;z).The concept of a pseudometric on X, thus, di�ers from the concept of ametric on X only in condition (PM1). The inclusion t� � t implies that t�j� � tj�. keywords: continuous; linear; order; satis; separable; set; sets; topology cache: agt-3024.pdf plain text: agt-3024.txt item: #344 of 431 id: agt-3025 author: Grinc, M.; Snoha, L. title: Jungck theorem for triangular maps and related results date: 2000-10-01 words: 4458 flesch: 80 summary: By Lemma 2.1 there exists a map f1 2 C(I;I) and �;� 2 Isuch that � � a1 � � and Coin(f1;g1) 83 - 92 Jungck theorem for triangular maps andrelated resultsM. Grin�c,� �L. SnohayAbstract. keywords: map; point; triangular; xed cache: agt-3025.pdf plain text: agt-3025.txt item: #345 of 431 id: agt-3026 author: Bosi, Gianni; Isler, Romano title: Separation axioms in topological preordered spaces and the existence of continuous order-preserving functions date: 2000-10-01 words: 2200 flesch: 60 summary: Since � is C-continuous, Anand Bn are closed subsets of X for every n 2 N. Further, An and Bn are disjointsets for every n 2 N (otherwise, for some n 2 N there exist x 2 X, a0n 2 A0n andb0n 2 B0n such that b0n � x � a0n, and therefore b0n 2 d(a0n)). = fG0nr : r 2 Sng such that A0n � G0nr � X ni(B0n)for every r 2 Sn n f1g. keywords: continuous; space cache: agt-3026.pdf plain text: agt-3026.txt item: #346 of 431 id: agt-3027 author: Künzi, Hans-Peter A. title: Preservation of completeness under mappings in asymmetric topology date: 2000-10-01 words: 8945 flesch: 74 summary: Suppose that the graph of F is �(U�1) � �(V�1)-closed. Furthermore for each� 2 D with j�j � 2 set B� = fx 2 S���(Ti2�(Ui)j�j)(B�) : (\i2�V �1i (y)) keywords: complete; completeness; metric; quasi; space; uniform; � lter cache: agt-3027.pdf plain text: agt-3027.txt item: #347 of 431 id: agt-3028 author: Höhle, Ulrich; Porst, Hans-E.; Sostak, Alexander P. title: Fuzzy functions: a fuzzy extension of the category SET and some related categories date: 2000-10-01 words: 5694 flesch: 82 summary: It is well knownthat every GL-monoid is residuated, i.e. there exists a further binary operation- implication \7�! such that� � � � () � � � 7�! 8�;�; 2 L:We set �2 = � � � and further by induction: �n = �n�1 � �. Then there would exist x0 2 X such that F(x;y) 6� � for each y 2 Z.On the other hand, from �(F) � � � �, it follows that for each x 2 X, inparticular, for x0 there exists y0 2 Y such that F(x0;y0) � �. keywords: category; f(x;y; fuzzy cache: agt-3028.pdf plain text: agt-3028.txt item: #348 of 431 id: agt-3029 author: Singh, D.; Kohli, J.K. title: R-spaces and closedness/completeness of certain function spaces in the topology of uniform convergence date: 2014-08-04 words: 5254 flesch: 78 summary: Section 6 is devoted to the study of function spaces wherein it is shown that the function space of all Rcl(X, Y ) of all Rcl-supercontinuous func- tions from a topological space X into a uniform space Y is closed in Y X in the topology of uniform convergence and the condition for its completeness is outlined. [26] S. A. Naimpally, Graph topology for function spaces, Trans. keywords: rcl; set; sets; space cache: agt-3029.pdf plain text: agt-3029.txt item: #349 of 431 id: agt-3045 author: Haouati, Afef; Lazaar, Sami title: Primal spaces and quasihomeomorphisms date: 2015-10-01 words: 4398 flesch: 86 summary: It follows immediately, from the fact that a map between two principal spaces is continuous if and only if the induced map between the associated quasi-ordered sets is isotone, that for every x, y ∈ X, we have: x ≤ y ⇒ f(x) We can easily see that for any set A of X, the closure A is exactly ∪[fn(A) : n ∈ N] and in particular for any point x ∈ X, {x} = {fn(x), n ∈ N} denoted Of (x) and called the orbit of x by f. keywords: q(x cache: agt-3045.pdf plain text: agt-3045.txt item: #350 of 431 id: agt-3141 author: Dridi, Lobna; Mhemdi, Abdelwaheb; Turki, Tarek title: F-nodec spaces date: 2015-03-23 words: 5515 flesch: 86 summary: In particular for any point x ∈ X, {x} = Of (x) = {fn(x) : n ∈ N} called the orbit of x by f. Alexandroff Topology According to Kennisson, a flow in a category C is a couple (X, f), where X is an object of C and f : X −→ X is a morphism, called the iterator (see [9] and [10]). keywords: nodec; space; subset cache: agt-3141.pdf plain text: agt-3141.txt item: #351 of 431 id: agt-3156 author: Losert, Bernd; Richardson, Gary title: Convergence S-compactifications date: 2014-07-25 words: 8959 flesch: 79 summary: F ∈ F}. ⊆ θ(cl F × G) for arbitrary F ∈ F and G ∈ G. Let 〈v, a〉 ∈ h−1(θY (cl f(F) keywords: compactification; f(x cache: agt-3156.pdf plain text: agt-3156.txt item: #352 of 431 id: agt-3157 author: Fernández, Manuel; Tkachenko, Mikhail title: Subgroups of paratopological groups and feebly compact groups date: 2014-07-21 words: 7496 flesch: 73 summary: 2(2014), 235-248doi:10.4995/agt.2014.3157 c© AGT, UPV, 2014 Subgroups of paratopological groups and feebly compact groups Manuel Fernández a and Mikhail Tkachenko1 b a Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, C.P. 09790, México, D.F. (mafevil5@gmail.com, manuel.fernandezvillanueva@uacm.edu.mx) b Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, México, D.F. (mich@xanum.uam.mx) Introduction Our aim is to study closures of subgroups of paratopological groups. keywords: group; group g; paratopological; precompact; set cache: agt-3157.pdf plain text: agt-3157.txt item: #353 of 431 id: agt-3161 author: Karlova, Olena title: On C-embedded subspaces of the Sorgenfrey plane date: 2015-02-02 words: 4788 flesch: 88 summary: Since cm → x ∗ in Sn+1, cm ∈ F and F is closed in Sn+1, x∗ ∈ F ∩ ( ∞ ⋂ m=0 Vm ) . Um = F ∩ n+1 ∏ k=1 [am,k, bm,k); 2) am ∈ F , cm ∈ U + m ∩ F ; 3) Vm+1 = F ∩ n+1 ∏ k=1 [am,k, cm,k); 4) Vm+1 ⊆ keywords: set cache: agt-3161.pdf plain text: agt-3161.txt item: #354 of 431 id: agt-3181 author: Bhattacharjee, Papiya; Knox, Michelle L.; McGovern, Warren Wm. title: The classical ring of quotients of $C_c(X)$ date: 2014-07-15 words: 3646 flesch: 83 summary: For r ∈ R notice that by the construction of X, if (σ, r) ∈ X, then for all σ ≤ τ Let K be a clopen subset of X such that π(K) is cofinal in W. Define the following sets for r ∈ R and ǫ > 0: Sǫr = {σ ∈ W : ({σ} × (r − ǫ, r + ǫ)) ∩ X ⊆ K} and TK = {r ∈ R : S ǫ r is cofinal in W for some ǫ > 0}. keywords: subset cache: agt-3181.pdf plain text: agt-3181.txt item: #355 of 431 id: agt-3242 author: Felicit, J. Maria; Eldred, A. Anthony title: Best Proximity Points for Cyclical Contractive Mappings date: 2015-10-01 words: 3469 flesch: 92 summary: Since ‖T p(mk+1)x0 − T p(nk+1)+1x0‖ ≤ ‖T pmk+1x0 − T pnk+2x0‖, ‖T pmkx0 − T pnk+1x0‖ ≤ ‖T pmkx0 − T p(mk+1)x0‖ + ‖T p(mk+1)x0 −T p(nk+1)+1x0‖ + ‖T p(nk+1)+1x0 − T pnk+1x0‖ ≤ ‖T pmkx0 − T p(mk+1)x0‖ +‖T pmk+1x0 − T pnk+2x0‖ +‖T p(nk+1)+1x0 − T pnk+1x0‖ ≤ ‖T pmkx0 − T p(mk+1)x0‖ +ψ(‖T pmkx0 − T pnk+1x0‖ −d(Ai,Ai+1)) Suppose for some n, xpn = y0, then xpn+1 = Txpn = Ty0, Assume xpn 6= y0 for any n. Since ‖T ny0 − T n+1y0‖ = d(Ai,Ai+1) and T py0 = y0, by cyclical proximal property. keywords: ai+1; d(ai cache: agt-3242.pdf plain text: agt-3242.txt item: #356 of 431 id: agt-3244 author: Aurichi, Leandro Fiorini; Bella, Angelo title: When is a space Menger at infinity? date: 2015-02-02 words: 2842 flesch: 83 summary: Since βX \ X is Menger, there is an f : ω −→ ω such that βX \ X ⊂ ⋃ n∈ω V n f(n) . Let K ⊂ X be a compact subset. keywords: infinity; menger; space cache: agt-3244.pdf plain text: agt-3244.txt item: #357 of 431 id: agt-3247 author: Acharyya, Sudip Kumar; Chattopadhyay, Kshitish Chandra; Rooj, Pritam title: A generalized version of the rings CK(X) and C∞(X)– an enquery about when they become Noetheri date: 2015-02-10 words: 3542 flesch: 79 summary: We get the familiar ring C(X) on choosing F = R. X is called completely F-regular (CFR in short) if given a closed set K in X and a point x ∈ X−K, there exists an f ∈ C(X, F) such that f(x) = 0 and f(K) Fn ≡ F × F × · · · × F (n times). keywords: ring cache: agt-3247.pdf plain text: agt-3247.txt item: #358 of 431 id: agt-3312 author: Comfort, W. W.; Gould, Franklin R. title: Some classes of minimally almost periodic topological groups date: 2015-10-01 words: 13225 flesch: 79 summary: group G into a compact group K, the continuous map φ : To see this, note that when G ∈ SSGP(n) and U ∈ N(1G) then we have, taking H := {{1G}}, that H := 〈 ⋃ H〉 = {1G} and G/H ≃ G ∈ SSGP(n), so indeed G ∈ SSGP(n + 1). keywords: abelian; group; group g; m.a.p; ssgp(n; theorem; topological; topology cache: agt-3312.pdf plain text: agt-3312.txt item: #359 of 431 id: agt-3323 author: Ozcag, Selma title: Lebesgue quasi-uniformity on textures date: 2015-10-01 words: 7674 flesch: 79 summary: Since (S, S) is plain and C is an anchored dicover, for s ′ ∈ S♭ we have Aj(s) [s ′ k] = d → sk Ps′ k gives Pz * Qz′ for z ′ ∈ S♭ and (2.2) dsk * Q(v,z′) =⇒ Ps′k ⊆ Qv, for v ∈ S ♭ From P (s′ k ,z) ⊆ dsk and keywords: lebesgue; quasi; uniformity cache: agt-3323.pdf plain text: agt-3323.txt item: #360 of 431 id: agt-3371 author: Nguemo, Miradain Atontsa; Tcheka, Calvin title: Sheaf cohomology on network codings: maxflow-mincut theorem date: 2017-10-02 words: 4238 flesch: 79 summary: dimN ≥ 0, hence dimH0(X;F) ≤ dimH0(D;F), for all open D and network coding sheaf F on the graph X. Keywords: network information flow; network coding sheaves; topological cut; relative sheaf cohomology. keywords: coding; graph; network; open; sheaf; theorem cache: agt-3371.pdf plain text: agt-3371.txt item: #361 of 431 id: agt-3424 author: Sultana, Asrifa; Vetrivel, V. title: Best proximity points of contractive mappings on a metric space with a graph and applications date: 2017-04-03 words: 4177 flesch: 87 summary: A0 = {x ∈ A : d(x,y) = d(A,B) for some y ∈ B} B0 = {y ∈ B : d(x,y) = d(A,B) for some x ∈ A}. X → X be a map such that for all x,y ∈ X with (x,y) ∈ E(G), (fx,fy) ∈ E(G) and d(fx,fy) ≤ kd(x,y) where k ∈ keywords: e(g; point cache: agt-3424.pdf plain text: agt-3424.txt item: #362 of 431 id: agt-3439 author: Hernández, Constancio; Rodríguez Medina, Leonardo; Tkachenko, Mikhail title: Baire property in product spaces date: 2015-02-05 words: 6590 flesch: 80 summary: ∗The research is partially supported by Consejo Nacional de Ciencias y Tecnoloǵıa (CONACyT), grant CB-2012-01-178103 Received 10 August 2013 – Accepted 10 August 2014 http://dx.doi.org/10.4995/agt.2015.3439 C. Hernández, L. Rodŕıguez Medina and M. Tkachenko The class of Baire spaces is closed under taking open subspaces as well as Gδ- dense subspaces. Also, images of Baire spaces under open continuous mappings and, more generally, under d-open mappings (see [23]) are Baire. keywords: baire; open; product; set; skeletal; spaces cache: agt-3439.pdf plain text: agt-3439.txt item: #363 of 431 id: agt-3445 author: Karamzadeh, O. A. S.; Namdari, M.; Soltanpour, S. title: On the locally functionally countable subalgebra of C(X) on locally functionally countable subalgebra of C(X) date: 2015-10-01 words: 13610 flesch: 86 summary: If f, g ∈ Lc(X) and Z(f) is a neighborhood of Z(g), then f = gh for some h ∈ Lc(X). f ∈ Lc(X)}, ZF (X) = {Z(f) : keywords: cc(x; ideal; lc(x; proposition; soc; space cache: agt-3445.pdf plain text: agt-3445.txt item: #364 of 431 id: agt-3584 author: Protasov, Igor V.; Slobodianiuk, Sergii title: The dynamical look at the subsets of a group date: 2015-10-01 words: 4186 flesch: 88 summary: A topological space X is called a G-space if there is the action X × G → X : (x, g) 7→ xg such that, for each g ∈ G, the mapping X → X : x 7→ xg is continuous. ∈ G}, T (x) = clO(x), W(x) = {y ∈ T (X) : keywords: group; subset cache: agt-3584.pdf plain text: agt-3584.txt item: #365 of 431 id: agt-3919 author: Gupta, Ankit; Sarma, Ratna Dev title: A uniform approach to normality for topological spaces date: 2016-04-12 words: 4699 flesch: 85 summary: The set A is called θ-closed if A = clθA. The complement of a θ-closed set is called θ-open set. In the literature, several such classes are available which include amongst others semi-open sets [10], α-open sets [12], β-open sets [1], pre-open sets [11], etc. keywords: open; set cache: agt-3919.pdf plain text: agt-3919.txt item: #366 of 431 id: agt-4085 author: Ekmekçi, Ramazan; Ertürk, Rıza title: Convergence in graded ditopological texture spaces date: 2016-04-12 words: 9690 flesch: 87 summary: For a texture (S, S), most properties are conveniently defined in terms of the p − sets Ps = ⋂ {A ∈ S | s ∈ A} and the q − sets Qs = ∨ {A ∈ S | s 6∈ A} = ∨ {Pu | u ∈ S, s 6∈ Pu}. The sets Ps, s ∈ S are molecules, and the texture (S, S) is called ”simple” if all molecules of S are in the form {Ps | s ∈ S}. keywords: texture cache: agt-4085.pdf plain text: agt-4085.txt item: #367 of 431 id: agt-4092 author: García-Máynez, Adalberto; Pimienta Acosta, Adolfo title: A note on unibasic spaces and transitive quasi-proximities date: 2017-04-03 words: 3712 flesch: 80 summary: It is enough to prove that C1 = C. If x ∈ X \ C, there exists a set B ∈ B such that x ∈ B ⊆ X \ C. Therefore, X \B ∈ C(B) and X \B ⊇ C, that is, {x}δC and X \C ⊆ X \C1. On the other hand, if x ∈ X \C1, i.e., if {x}δC, there exists a set H ∈ C(B) such that H ⊇ C y x 6∈ H. Therefore, x ∈ X \C and the proof is complete. keywords: quasi cache: agt-4092.pdf plain text: agt-4092.txt item: #368 of 431 id: agt-4154 author: Sharma, Puneet title: Induced dynamics on the hyperspaces date: 2016-10-03 words: 6292 flesch: 72 summary: A point x is called periodic for if there exists n ∈ N such that x ∈ F n(x). ∈ F n(x) for any member f of F . keywords: dynamics; hyperspace; set; system; topology cache: agt-4154.pdf plain text: agt-4154.txt item: #369 of 431 id: agt-4163 author: Benterki, Abdessalem title: A local fixed point theorem for set-valued mappings on partial metric spaces date: 2016-04-12 words: 5199 flesch: 84 summary: 17, no. 1(2016), 37-49doi:10.4995/agt.2016.4163 c© AGT, UPV, 2016 A local fixed point theorem for set-valued mappings on partial metric spaces Abdessalem Benterki LAMDA-RO Laboratory, Department of Mathematics, University of Blida, Algeria LMP2M Laboratory, University of Medea, Algeria (benterki.abdessalem@gmail.com) Abstract The purpose of this paper is to study the existence and location of fixed points for pseudo-contractive-type set-valued mappings in the setting of partial metric spaces by using Bianchini-Grundolfi gauge functions. keywords: metric; p(x; point; theorem cache: agt-4163.pdf plain text: agt-4163.txt item: #370 of 431 id: agt-4220 author: Das, Ananga Kumar; Bhat, Pratibha title: A decomposition of normality via a generalization of $\kappa$-normality date: 2017-10-02 words: 4908 flesch: 77 summary: Every almost regular, θ-normal space is π-normal. [11] L. N. Kalantan, π-Normal topological spaces, Filomat 22, no. 1 (2008), 173–181. keywords: normal; space cache: agt-4220.pdf plain text: agt-4220.txt item: #371 of 431 id: agt-4401 author: Garrido, Isabel; Meroño, Ana S. title: Two classes of metric spaces date: 2016-04-12 words: 6344 flesch: 81 summary: 17, no. 1(2016), 57-70 doi:10.4995/agt.2016.4401 c© AGT, UPV, 2016 Two classes of metric spaces M. Isabel Garrido a,∗ and Ana S. Meroño b,∗ a Instituto de Matemática Interdisciplinar (IMI), Departamento de Geometŕıa y Topoloǵıa, Uni- versidad Complutense de Madrid, 28040 Madrid, Spain (maigarri@mat.ucm.es) b Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040-Madrid, Spain. Abstract The class of metric spaces (X, d) known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. keywords: metric; spaces cache: agt-4401.pdf plain text: agt-4401.txt item: #372 of 431 id: agt-4469 author: de la Barrera Mayoral, Daniel title: Non metrizable topologies on Z with countable dual group. date: 2017-04-03 words: 5487 flesch: 80 summary: The family Bb := {bnZ : n ∈ N0} is a neighborhood basis of 0 for a linear (that is, it has a neighborhood basis consisting in open subgroups) group topology on Z, which will be called b-adic topology and is denoted by λb. [8] M. J. Chasco, E. Mart́ın-Peinador and V. Tarieladze, On Mackey topology for groups, Stud. keywords: group; let; sequence; topology cache: agt-4469.pdf plain text: agt-4469.txt item: #373 of 431 id: agt-4495 author: Grecova, Svetlana; Sostak, Alexander P.; Uljane, Ingrida title: A construction of a fuzzy topology from a strong fuzzy metric date: 2016-10-03 words: 6083 flesch: 79 summary: Fuzzy topologies. In case when L = [0, 1] and when we do not specify the range M we will call [0, 1], [0, 1]-fuzzy topologies just as fuzzy topologies. keywords: fuzzy; metric; spaces; topology cache: agt-4495.pdf plain text: agt-4495.txt item: #374 of 431 id: agt-4521 author: Almontashery, Khulod; Kalantan, Lutfi title: Results about the Alexandroff duplicate space date: 2016-10-03 words: 2856 flesch: 79 summary: [9] L. Kalantan, π-normal topological spaces, Filomat 22, no. 1 (2008), 173–181. Consider Rω1, which is Tychonoff separable non-normal space ([5], 2.3.15). keywords: a(x; space cache: agt-4521.pdf plain text: agt-4521.txt item: #375 of 431 id: agt-4555 author: Shah, Sejal; Das, Ruchi; Das, Tarun title: A note on uniform entropy for maps having topological specification property date: 2016-10-03 words: 2393 flesch: 73 summary: A uniform structure on X is a non-empty set U of subsets of X × X satisfying the following conditions: i: if U ∈ U then △X ⊂ U, ii: if U ∈ U and U ⊂ V ⊂ X × X then V ∈ U, iii: if U ∈ U and V ∈ U then U ∩ V ∈ U, iv: if U ∈ U then UT ∈ U, v: if U ∈ U then there exists V ∈ U X × X| there exists z ∈ X satisfying (x, z) ∈ U and (z, y) ∈ V }. keywords: entropy cache: agt-4555.pdf plain text: agt-4555.txt item: #376 of 431 id: agt-4561 author: Bosi, Gianni; Caterino, Alessandro; Ceppitelli, Rita title: Normally preordered spaces and continuous multi-utilities date: 2016-04-12 words: 5050 flesch: 70 summary: We recall that a (not necessarily total) preorder � on a topological space (X,τ) admits a (continuous) multi-utility representation if there exists a family F of (continuous) increasing real functions on the preordered topological space Received 18 January 2016 – Accepted 16 March 2016 http://dx.doi.org/10.4995/agt.2016.4561 G. Bosi, A. Caterino and R. Ceppitelli (X,τ,�) such that, for all x,y ∈ X, x � y is equivalent to f(x) The preorder � is said to be total if for any two elements x,y ∈ X either x � y or y � x. Define, for every point x ∈ X, the sets d(x) := {y ∈ X | y � x} and i(x) := {z ∈ X | x � z}. keywords: space cache: agt-4561.pdf plain text: agt-4561.txt item: #377 of 431 id: agt-4616 author: Lipparini, Paolo title: The equivalence of two definitions of sequential pseudocompactness date: 2016-04-12 words: 2001 flesch: 64 summary: A product of nonempty topological spaces is sequen- tially feebly compact if and only if each factor is sequentially feebly compact. Keywords: sequentially pseudocompact; feebly compact; topological space. keywords: pseudocompact cache: agt-4616.pdf plain text: agt-4616.txt item: #378 of 431 id: agt-4624 author: Boxer, Laurence; Staecker, P. Christopher title: Fundamental groups and Euler characteristics of sphere-like digital images date: 2016-10-03 words: 8989 flesch: 78 summary: Digital fundamental group. For closed digital surfaces X and Y , we have χ(X♯Y ) keywords: digital; homotopy; loop; theorem cache: agt-4624.pdf plain text: agt-4624.txt item: #379 of 431 id: agt-4676 author: Hattab, Hawete title: On quasi-orbital space date: 2017-04-03 words: 3301 flesch: 83 summary: Keywords: homeomorphism; group; quasi-orbit space; quasi-orbital space. On quasi-orbital space the induced subgroup of G on S. Since S is an invariant subset of E, we have for each x ∈ S, H(x) = G(x). keywords: compact; space; subset cache: agt-4676.pdf plain text: agt-4676.txt item: #380 of 431 id: agt-4704 author: Boxer, Laurence; Ege, Ozgur; Karaca, Ismet; Lopez, Jonathan; Louwsma, Joel title: Digital fixed points, approximate fixed points, and universal functions date: 2016-10-03 words: 6765 flesch: 78 summary: [23] introduced the notion of a digitally continuous func- tion between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. Keywords: digital image; digitally continuous; digital topology; fixed point. keywords: digital; function; point cache: agt-4704.pdf plain text: agt-4704.txt item: #381 of 431 id: agt-5180 author: Komal, Somayya; Kumam, Poom title: Global optimization using $\alpha$-ordered proximal contractions in metric spaces with partial orders date: 2016-10-03 words: 3996 flesch: 77 summary: 17, no. 2 176 Global optimization using α-ordered proximal contractions in metric spaces with partial orders Then there exists a point x ∈ A and a point y ∈ B such that d(gx,Sx) = d(gy,Ty) = d(x,y) = d(A,B). Then there exists a point x ∈ A and a point y ∈ B such that d(x,Sx) = d(y,Ty) = d(x,y) = d(A,B). keywords: d(a cache: agt-5180.pdf plain text: agt-5180.txt item: #382 of 431 id: agt-5185 author: Dung, Nguyen Van; Le Hang, Vo Thi; Dolicanin-Djekic, Diana title: An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces date: 2017-10-02 words: 6119 flesch: 80 summary: � Though many results in C∗-algebra valued metric spaces and C∗-algebra valued b-metric spaces are consequences of certain results in metric spaces or in b-metric spaces, we must say that we do not know whether the Caristi’s fixed point theorem in C∗-algebra valued metric spaces [25, Theorem 3.5] may be deduced from Caristi’s fixed point theorem in metric spaces Is it possible to derive Caristi’s fixed point theorem in C∗-algebra valued metric spaces [25, Theorem 3.5] from Caristi’s fixed point theorem in metric spaces [8, Theorem 1]? Acknowledgements. keywords: c∗-algebra; metric; point; space cache: agt-5185.pdf plain text: agt-5185.txt item: #383 of 431 id: agt-5660 author: Komal, Somayya; Kumam, Poom; Gopal, Dhananjay title: Best Proximity point for Z-contraction and Suzuki type Z-contraction mappings with an application to fractional calculus date: 2016-10-03 words: 5428 flesch: 85 summary: Also by the help of weak P-property and P-property, we proved existence and uniqueness of best proximity point. Keywords: best proximity point; weak P-property; Suzuki type Z- contraction; functional differential equation. keywords: contraction; d(a; point cache: agt-5660.pdf plain text: agt-5660.txt item: #384 of 431 id: agt-5818 author: Olela Otafudu, Olivier; Sabao, Hope title: On quasi-uniform box products date: 2017-04-03 words: 5631 flesch: 88 summary: Let (X,U) be a quasi-uniform space and ∏ α∈N X be the product set of countably many copies of X. Then Ǔα = {Ǔα : U ∈ U and α ∈ N} is a filter base generating a quasi-uniformity on ∏ α∈N X, where Ǔα = { (x,y) ∈ ∏ β∈N X × ∏ β∈N X : (x(α),y(α)) Then U = {U : U ∈ U} is a filter base generating a quasi-uniformity on ∏ α∈N X where U = { (x,y) ∈ ∏ α∈N X × ∏ α∈N X : (x(α),y(α)) keywords: quasi; uniform; α∈n cache: agt-5818.pdf plain text: agt-5818.txt item: #385 of 431 id: agt-5868 author: Stadler, Baerbel M R; Stadler, Peter F. title: Oriented components and their separations date: 2017-10-02 words: 11010 flesch: 81 summary: Qp for p ∈ P such that ⋃ p∈P Qp = Q. (d) From A |̇ B we know that for all P ≻− Q with P ∪ Q ⊆ keywords: q[p cache: agt-5868.pdf plain text: agt-5868.txt item: #386 of 431 id: agt-5869 author: Sari, Dewi Kartika; Zhao, Dongsheng title: A new cardinal function on topological spaces date: 2017-04-03 words: 7736 flesch: 90 summary: As remarked at the beginning of the Section 2, all spaces considered in this paper are non-empty. Recall from [2] that a mapping f : X → Y from a topological space X to a topological space Y is said to be M-uniformly continuous, if for every λ ∈ ∆(Y ) there exists δ ∈ ∆(X) such that for any x,y ∈ X, x ≺Mδ y implies f(x) ≺Mλ f(y). Let A,B be non-empty subsets of space X and δ ∈ ∆(X). keywords: finite; gauge; gci(x; set; space; topology cache: agt-5869.pdf plain text: agt-5869.txt item: #387 of 431 id: agt-5920 author: Nazam, Muhammad; Arshad, Muhammad; Abbas, Mujahid title: Some fixed point results for dualistic rational contractions date: 2016-10-03 words: 3919 flesch: 84 summary: + βd(j,k), for all comparable j,k ∈ M with j 6= k and 0 < α + β < 1. + βd(j,k), for all comparable j,k ∈ M with j 6= k and 0 < α + β < 1. keywords: metric cache: agt-5920.pdf plain text: agt-5920.txt item: #388 of 431 id: agt-6322 author: Mongkolkeha, Chirasak; Cho, Yeol Je; Kumam, Poom title: Fixed point theorems for simulation functions in b-metric spaces via the wt-distance date: 2017-04-03 words: 6180 flesch: 85 summary: A function p : X ×X → [0,∞) defined by p(x,y) = c for all x,y ∈ X is a w-distance on X, where c is a positive real number. A function p : X×X → [0,∞) defined by p(x,y) = ‖x‖ + ‖y‖ for all x,y ∈ X is a w-distance on X. Example 2.7. keywords: distance; lim; metric cache: agt-6322.pdf plain text: agt-6322.txt item: #389 of 431 id: agt-6376 author: Krebs, Mike title: On cardinalities and compact closures date: 2017-04-03 words: 4595 flesch: 84 summary: For y ∈ X, we define the closed ray (−∞,y] := {x ∈ X | x ≤ y} and the open ray (−∞,y) := {x ∈ X | x < y}. Recall that if A is a Hausdorff topological space and p is a point not in A, then we define the co-compact topology on A∪{p} by choosing the neighborhood basis at p to consist of all complements of compact subsets of A. The definition of Ny is somewhat similar to this; we take the neighborhood basis at y to be the collection of all complements of closed sets, every “small” closed subset of which is compact. keywords: compact; set; topology cache: agt-6376.pdf plain text: agt-6376.txt item: #390 of 431 id: agt-6578 author: Phuengrattana, Withun title: On the generalized asymptotically nonspreading mappings in convex metric spaces date: 2017-04-03 words: 4499 flesch: 79 summary: [14] introduced a nonlinear mapping called nonspreading mapping in a smooth, strictly convex, and reflexive Banach space X as follows: Let C be a nonempty closed convex subset of X. A mapping Received 09 September 2016 – Accepted 24 December 2016 http://dx.doi.org/10.4995/agt.2017.6578 W. Phuengrattana T : C → C is said to be nonspreading if φ(Tx,Ty) + φ(Ty,Tx) ≤ φ(Tx,y) + φ(Ty,x)(1.1) for all x,y ∈ C, where φ(x,y) = ‖x‖2 − 2〈x,Jy〉 + ‖y‖2 for all x,y ∈ X and J is the duality mapping on C. Observe that if X is a real Hilbert space, then J is the identity mapping and φ(x,y) = ‖x−y‖2 for all x, [9] S. Iemoto, K. Takahashi and W. Takahashi, A weak convergence theorem for nonexpan- sive mappings and nonspreading mappings in a Hilbert space, In: Akashi, S., Takahashi, W., Tanaka, T. (eds.) keywords: convex cache: agt-6578.pdf plain text: agt-6578.txt item: #391 of 431 id: agt-6644 author: Dube, Themba title: A note on weakly pseudocompact locales date: 2017-04-03 words: 5147 flesch: 80 summary: In locales the Baire property cannot be defined by decreeing that countable intersections of open dense sublocales be dense, because all intersections of dense sublocales are dense. The reason is that O(X × Y ) is isomorphic to a dense sublocale of OX ⊕ OY [17, Proposition IV 5.4.1], and a locale which has dense pseudocompact sublocale is pseudocompact keywords: frame; pseudocompact; sublocale cache: agt-6644.pdf plain text: agt-6644.txt item: #392 of 431 id: agt-6663 author: Boxer, Laurence title: Digital shy maps date: 2017-04-03 words: 4385 flesch: 78 summary: Further remarks We have made several contributions to our knowledge of digital shy maps. Let f : (A,κ) → (B,λ) and g : (B,λ) → (C,µ) be continuous functions between digital images. keywords: digital cache: agt-6663.pdf plain text: agt-6663.txt item: #393 of 431 id: agt-6694 author: Onsod, Wudthichai; Kumam, Poom; Cho, Yeol Je title: Fixed points of α-Θ-Geraghty type and Θ-Geraghty graphic type contractions date: 2017-04-03 words: 7224 flesch: 86 summary: [θ(β(N(x,y))N(x,y))]k, for all x,y ∈ X, where N(x,y) = max{p(x,y),p(x,Tx),p(y,Ty)} . Define a function α : X ×X → [0,∞) by α(x,y) = { 1, if x,y ∈ X, 0, otherwise, define two mappings S,T : keywords: point cache: agt-6694.pdf plain text: agt-6694.txt item: #394 of 431 id: agt-6713 author: Bisht, Ravindra K.; Pant, R. P. title: Contractive definitions and discontinuity at fixed point date: 2017-04-03 words: 4290 flesch: 86 summary: Keywords: Fixed point; (�−δ) contractions; power contraction; orbital con- tinuity. This implies that Txn → z = Tz and T is continuous at the fixed point z. Kannan’s paper generated a far-flung interest in the study of fixed points of generalized contractive mappings and soon these were followed by a flood of pa- pers involving contractive definitions, many of which did not require continuity of the mapping. keywords: point cache: agt-6713.pdf plain text: agt-6713.txt item: #395 of 431 id: agt-6716 author: Bell, Kathleen; Richmond, Thomas A. title: Transitions between 4-intersection values of planar regions date: 2017-04-03 words: 10719 flesch: 79 summary: A◦ ∩ B◦ and ∂A ∩ B◦, (c) ∂A ∩ ∂B and A◦ ∩ B◦, (d) ∂A ∩ B◦, and (e) ∂A ∩ ∂B and A◦ ∩ B◦ and ∂A∩B◦. By continuity, a(0) = b(0), so A◦(0) and B◦(0) have the same positive area and either B◦(0) ⊆ keywords: a(t; area; b(t; value cache: agt-6716.pdf plain text: agt-6716.txt item: #396 of 431 id: agt-6797 author: Thivagar, M. Lellis; Reilly, Ivan L.; Dasan, M. Arockia; Ramesh, V. title: Generalized open sets in grill N-topology date: 2017-10-02 words: 5274 flesch: 90 summary: Let X be a non empty set, τ1, τ2, ... , τN be N-arbitrary topologies defined on X and let the collection Nτ be defined by Nτ = {S ⊆ X : S = ( ⋃ N i=1 Ai) ∪ ( ⋂ N i=1 Bi), Ai, Bi ∈ τi}, satisfying the following axioms: (i) X, ∅ ∈ Nτ (ii) ⋃ ∞ i=1 Si ∈ Nτ for all {Si} ∞ i=1 ∈ Nτ (iii) ⋂ n i=1 Si ∈ Nτ for all {Si} n i=1 ∈ Nτ. ∈ Nτ and A∪B /∈ keywords: open cache: agt-6797.pdf plain text: agt-6797.txt item: #397 of 431 id: agt-6889 author: Dost, Senol title: Metric spaces and textures date: 2017-04-03 words: 6966 flesch: 84 summary: Qv for some v ∈ U. By the definition of Nρ� (u), there exists y,z ∈ U such that ρ(u,v) + ρ(v,z), (u,v,z ∈ U) keywords: spaces; texture cache: agt-6889.pdf plain text: agt-6889.txt item: #398 of 431 id: agt-7012 author: Al Shumrani, M. A. title: Partially topological group action date: 2018-04-02 words: 3059 flesch: 75 summary: [4] A. Piękosz, On generalized topological spaces I, Ann. [5] A. Piękosz, On generalized topological spaces II, Ann. keywords: action; group; space cache: agt-7012.pdf plain text: agt-7012.txt item: #399 of 431 id: agt-7048 author: Alqurash, Wafa Khalaf; Khan, Liaqat Ali title: Quasi-uniform convergence topologies on function spaces- Revisited date: 2017-10-02 words: 8189 flesch: 88 summary: Equivalently, for each y ∈ Y , the collection By = {U[y] : U ∈ U} forms a local base at y for the topology T (U). If U ∈ U, there is some V ∈ U such that V 2 ⊆ U. In this case, the pair (Y, U) is called a quasi-uniform space. keywords: f(x; let; quasi; space; uniform; ∈ u cache: agt-7048.pdf plain text: agt-7048.txt item: #400 of 431 id: agt-7061 author: Rubin, Leonard R. title: Topological n-cells and Hilbert cubes in inverse limits date: 2018-04-02 words: 6782 flesch: 79 summary: We shall demonstrate, Proposition 2.7, that if X = (|Ka|, p b a, (A, �)) is an inverse system in set theory of triangulated polyhedra |Ka| with simplicial bonding functions pba, and X = lim X, then there exists a uniquely determined sub-inverse system XX = (|La|, p b a ∣ ∣|Lb|, (A, �)) of X where for each a, La is a subcomplex of Ka, each p b a ∣ ∣|Lb| : |Lb| → |La| is surjective, and lim XX = X. 1In this paper map means continuous function. If X = lim X, then pa : X → Xa will denote the a-coordinate projection. keywords: dim; inverse; lim cache: agt-7061.pdf plain text: agt-7061.txt item: #401 of 431 id: agt-7067 author: Choban, Mitrofan M.; Berinde, Vasile title: Multiple fixed point theorems for contractive and Meir-Keeler type mappings defined on partially ordered spaces with a distance date: 2017-10-02 words: 7497 flesch: 77 summary: On the other hand, in 2010, Samet and Vetro [74] apart of some coupled fixed point results they have established, considered a concept of fixed point of m-order as a natural extension of the notion of coupled fixed point. After these starting papers, a substantial number of articles were dedicated to the study of triple fixed points, quadruple fixed points, as well as to multiple fixed points (also called fixed point of m-order, or ”a multidimensional fixed point”, or ”an m-tuplet fixed point”, or ”an m-tuple fixed point”), see [1], [2], [7], [48], [49], [50], [53], [60], [67]-[72], [81], [83], [86], which form a very selective list contributions. keywords: distance; metric; point; spaces; theorems cache: agt-7067.pdf plain text: agt-7067.txt item: #402 of 431 id: agt-7146 author: Boxer, Laurence title: Alternate product adjacencies in digital topology date: 2018-04-02 words: 15441 flesch: 87 summary: • F has weak continuity if for each pair of adjacent x, y ∈ X, f(x) and f(y) are adjacent subsets of Y . Gen. Topol. 19, no. 1 27 L. Boxer • F has strong continuity if for each pair of adjacent x, y ∈ X, every point of f(x) is adjacent or equal to some point of f(y) and every point of f(y) is adjacent or equal to some point of f(x). keywords: digital; product cache: agt-7146.pdf plain text: agt-7146.txt item: #403 of 431 id: agt-7149 author: Gupta, Ankit; Sarma, Ratna Dev title: A study of function space topologies for multifunctions date: 2017-10-02 words: 6889 flesch: 80 summary: ⊆ V } where C is a compact subset of Y , y ∈ Y and V ∈ µ. Let SMco = {(C, V ) | C is compact in Y and V ∈ µ} and S M po = {(y, V ) | y ∈ Y, V ∈ µ}. Gen. Topol. 18, no. 2 (2017), 331-344doi:10.4995/agt.2017.7149 c© AGT, UPV, 2017 A study of function space topologies for multifunctions Ankit Gupta a,∗ and Ratna Dev Sarma b, † a Department of Mathematics, University of Delhi, Delhi 110007, India (ankitsince1988@yahoo.co.in) b Department of Mathematics, Rajdhani College, University of Delhi, Delhi 110015, India. keywords: cm(y; topology cache: agt-7149.pdf plain text: agt-7149.txt item: #404 of 431 id: agt-7257 author: Suantai, Suthep; Srisap, Kittipong; Naprang, Natthapong; Mamat, Manatsawin; Yundon, Vithoon; Cholamjiak, Prasit title: Convergence theorems for finding the split common null point in Banach spaces date: 2017-10-02 words: 5867 flesch: 93 summary: − xn − αn(f(xn) − xn) = γn(zn − xn).(3.7) − ‖x − u‖2 keywords: xn+1; − z0 cache: agt-7257.pdf plain text: agt-7257.txt item: #405 of 431 id: agt-7409 author: Abtahi, Mortaza; Kadelburg, Zoran; Radenovic, Stojan title: Fixed points and coupled fixed points in partially ordered ν-generalized metric spaces date: 2018-10-04 words: 5690 flesch: 84 summary: Let E be a nonempty set and ν ∈ N. A mapping dν : E × E → R + is called a ν-generalized metric and the pair (E, dν) is called a ν-generalized metric space if the following hold: (1) dν(x, y) = 0 if and only if x = y; (2) dν(x, y) = dν(y, x), for all x, y ∈ E; (3) dν(x, y) ≤ dν(x, z1) + dν(z1, z2) + · · · + dν(zν, y), for each set {x, z1, . . . Now, consider the mappings ρ+, ρmax : E × E → R + defined by ρ+(x, u) = dν(x, u) keywords: metric cache: agt-7409.pdf plain text: agt-7409.txt item: #406 of 431 id: agt-7452 author: Radhakrishnan, M.; Rajesh, S.; Agrawal, Sushama title: Some fixed point theorems on non-convex sets date: 2017-10-02 words: 6941 flesch: 93 summary: But, note that lim k→∞ ‖xnk − T xnk‖ = 0. ‖xnj − T keywords: t x1; t x2; t x3 cache: agt-7452.pdf plain text: agt-7452.txt item: #407 of 431 id: agt-7630 author: Alqurashi, Wafa Khalaf; Khan, Liaqat Ali; Osipov, Alexander V. title: Set-open topologies on function spaces date: 2018-04-02 words: 5220 flesch: 84 summary: A quasi-uniform space (Y, U) is called locally symmetric if, for each y ∈ Y and each U ∈ U, there is a symmetric V ∈ U such that V 2[y] ⊆ U[y] Recall that a net {yα : α ∈ D} in a quasi-uniform space (Y, U) is said to be T (U)-convergent to y ∈ Y if, for each U ∈ U, there exists an α0 ∈ D such that yα ∈ U[y] for all α ≥ α0. keywords: space; topology cache: agt-7630.pdf plain text: agt-7630.txt item: #408 of 431 id: agt-7638 author: Suantai, Suthep; Cho, Yeol Je; Tiammee, Jukrapong title: Common fixed points for generalized ψ-contractions in weak non-Archimedean fuzzy metric spaces date: 2019-04-01 words: 7008 flesch: 90 summary: The four couple (A,B;S,T) is called ψ-contractive mappings if there exists ψ ∈ Ψ such that, for all x,y ∈ X and t ∈ (0,∞) with M(x,y,t) > 0, the following condition holds: M(Ax,By,t) ≥ ψ(m(x,y,t)), where m(x,y,t) = min{M(Sx,Ty,t),M(Ax,Sx,t),M(By,Ty,t)}. Assume that there exists ψ ∈ Ψ such that, for all x,y ∈ X and t ∈ (0,∞) with M(x,y,t) > 0, the following condition holds: M(Ax,By,t) ≥ ψ(m(x,y,t)), where m(x,y,t) = min{M(x,y,t),M(Ax,x,t),M(y,By,t)}. keywords: fuzzy; m(x cache: agt-7638.pdf plain text: agt-7638.txt item: #409 of 431 id: agt-7667 author: Afrooz, Susan; Azarpanah, Fariborz; Etebar, Masoomeh title: On rings of real valued clopen continuous functions date: 2018-10-04 words: 8111 flesch: 84 summary: ∈ Cs(X), e(Qx) = 0, since Qx ⊆ U and e(A) = 1. (2) Whenever X is ultra Hausdorff and x, y ∈ X are distinct, then there exists a clopen set U containing x but not y. For a topological space X, the fixed maximal ideals in Cs(X) are precisely the sets MQx = {f ∈ Cs(X) : keywords: cs(x; set; space cache: agt-7667.pdf plain text: agt-7667.txt item: #410 of 431 id: agt-7673 author: Fallahi, Kamal; Abbas, Mujahid; Soleimani Rad, Ghasem title: Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results date: 2017-10-02 words: 5040 flesch: 83 summary: If there exist nonnegative constants α,β,γ such that q(Tx,Ty) � αq(x,y) + βq(x,Tx) + γq(y,Ty) for all x,y ∈ X, where x and y are e-close elements and s(α+β)+γ < If for all n ≥ 1, q(x,yn) � u for some u = ux, then q(x,y) � su, where {yn} is a sequence in X which converges to y ∈ X; (q4) for any c ∈ intP , there exists e ∈ E with keywords: cone; metric; spaces cache: agt-7673.pdf plain text: agt-7673.txt item: #411 of 431 id: agt-7677 author: Ahmadullah, Md; Imdad, Mohammad; Arif, Mohammad title: Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions date: 2018-04-02 words: 8137 flesch: 77 summary: Let (f, g) be a pair of self-mappings defined on a non-empty set X. Then (i) a point u ∈ X is said to be a coincidence point of the pair (f, g) if fu = gu, (ii) a point v ∈ X is said to be a point of coincidence of the pair (f, g) if there exists u ∈ X such that v = fu = gu, (iii) a coincidence point u ∈ X of the pair (f, g) is said to be a common fixed point if u = fu = gu, (iv) a pair (f, g) is called commuting if f(gu) = g(fu), ∀ u ∈ X. (v) a pair (f, g) is said to be weakly compatible if f and g commutes at their coincidence points i.e., f(gu) = g(fu) whenever f(u) = g(u) for any u ∈ X. Definition 2.2 ([17, 28, 27]). Then (u, v) ∈ Rs if and only if [u, v] ∈ R. Definition 2.6 ([4]). keywords: point; relation cache: agt-7677.pdf plain text: agt-7677.txt item: #412 of 431 id: agt-7731 author: Zamani Bahabadi, Alireza title: Controlled shadowing property date: 2018-04-02 words: 3650 flesch: 81 summary: Since f has controlled shadowing property by Theorem 3.8, f × f has controlled shadowing property. Keywords: controlled shadowing property; chaos; topologically ergodic; specification property; topologically mixing. keywords: property; shadowing cache: agt-7731.pdf plain text: agt-7731.txt item: #413 of 431 id: agt-7798 author: Boxer, Laurence title: Generalized Normal Product Adjacency in Digital Topology date: 2017-10-02 words: 12903 flesch: 83 summary: Zn and x ∈ X, the set of points adjacent to x ∈ Zn and the neighborhood of x in Zn are, respectively, Nκ(x) For a digital image (X, κ) ⊂ (Zn, κ), a function f : S(X, r) → Y induces a multivalued function F : X ⊸ Y if x ∈ X implies F(x) = ⋃ x′∈E −1 r (x) {f(x′)}. keywords: digital; function; theorem cache: agt-7798.pdf plain text: agt-7798.txt item: #414 of 431 id: agt-7812 author: Yildiz, Filiz title: Some categorical aspects of the inverse limits in ditopological context date: 2018-04-02 words: 13141 flesch: 71 summary: We define the joint topology on S in terms of its family Jcτκ of closed sets by the condition W ∈ Jcτκ ⇐⇒ (s ∈ S, G ∈ η(s),K ∈ µ(s) =⇒ G ∩ W 6⊆ K) Thus, because of the facts sα ∈ Sα, α ∈ Λ and ϕαβ(sα) = sβ for α ≥ β, the point s = {sα} becomes an element of S∞, obviously and this gives a contradiction. keywords: ifpditop; inverse; inverse systems; lim; limit; spaces; systems; theorem; α ∈ cache: agt-7812.pdf plain text: agt-7812.txt item: #415 of 431 id: agt-7849 author: Jäger, Gunther; Ahsanullah, T. M. G. title: Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence date: 2018-04-02 words: 7572 flesch: 83 summary: If d 6= d′ then, without loss of generality, there are x,y ∈ X such that d(x,y) 6≤ d′(x,y). A triple (X, ·,c), where (X, ·) is a group and (X,c) is an L-convergence tower space, is called an L-convergence tower group if for all x,y ∈ X and all F,G ∈ F(X) (LCTGM) keywords: convergence; metric; spaces cache: agt-7849.pdf plain text: agt-7849.txt item: #416 of 431 id: agt-7883 author: Yan, Peng-Fei; Hu, Xing-Yu; Xie, Li-Hong title: k-semistratifiable spaces and expansions of set-valued mappings date: 2018-04-02 words: 4017 flesch: 82 summary: Let K be a compact subset of Uϕ. By Proposition 2.5, there exists k ∈ N such that K ⋂ U(k Let K be a compact subset of X, then there exists k ∈ N such that K ⋂ U(k+ 1, (Fn,ϕ)) keywords: set cache: agt-7883.pdf plain text: agt-7883.txt item: #417 of 431 id: agt-7888 author: Bella, Angelo title: Few remarks on maximal pseudocompactness date: 2018-04-02 words: 3097 flesch: 75 summary: But then, {Un \ V : n < ω} would be a locally finite infinite family of open sets in (X, σ), in contrast with the pseudocompactness of σ. � The next observation shows that maximal pseudocompact spaces are “very close to” first countable. Example 2.14 in [1] as well as the space X in Example 2.9 above provide maximal pseudocompact spaces which are not wHMP. keywords: pseudocompact; space; γ(n cache: agt-7888.pdf plain text: agt-7888.txt item: #418 of 431 id: agt-7910 author: Ali Akbar, Kamaludheen; Kannan, V.; Subramania Pillai, I. title: Simple dynamical systems date: 2019-10-01 words: 8742 flesch: 82 summary: Keywords: special points; non-ordinary points; critical points; order conju- gacy. Let f, g be two increasing bijection on R with finitely many (same number of ) non-ordinary points. keywords: conjugacy; order; points; proposition cache: agt-7910.pdf plain text: agt-7910.txt item: #419 of 431 id: agt-7918 author: Pant, Rajendra title: Fixed point theorems for nonlinear contractions with applications to iterated function systems date: 2018-04-02 words: 4002 flesch: 89 summary: Gen. Topol. 19, no. 1 (2018), 163-172doi:10.4995/agt.2018.7918 c© AGT, UPV, 2018 Fixed point theorems for nonlinear contractions with applications to iterated function systems Rajendra Pant Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur 440010, India (pant.rajendra@gmail.com) Communicated by S. Romaguera Abstract We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Also we discuss an application to iterated function systems. keywords: function cache: agt-7918.pdf plain text: agt-7918.txt item: #420 of 431 id: agt-7955 author: Bovdi, Victor; Salim, Mohamed; Ursul, Mihail title: Completely simple endomorphism rings of modules date: 2018-10-04 words: 7241 flesch: 83 summary: Let ∏ α∈Ω Rα be a family of compact rings with identity. If αei 6= βei (α,β ∈ R), then there exists an element x = ∑ j rjvj ∈ Ap such that αei(x) 6= βei(x), hence, α(rivi) 6= β(rivi). keywords: end; finite; ring; topology cache: agt-7955.pdf plain text: agt-7955.txt item: #421 of 431 id: agt-7962 author: Gopal, Sharan; Ravulapalli, Srikanth title: Dynamics of real projective transformations date: 2018-10-04 words: 2805 flesch: 70 summary: Given x ∈ X, the sequence (x, f(x), f2(x), f3(x), ...) is called the trajectory of x, where fk(x) A point x ∈ X is said to be periodic if there is a k ∈ N such that fk(x) keywords: projective cache: agt-7962.pdf plain text: agt-7962.txt item: #422 of 431 id: agt-7997 author: Olela Otafudu, Olivier title: Some aspects of Isbell-convex quasi-metric spaces date: 2018-04-02 words: 6243 flesch: 91 summary: Moreover, we say that q is a T0-quasi-metric provided that it satisfies the additional condition that for any x,y ∈ X, q(x,y) = 0 = q(y,x) implies that x = y. The set X together with a T0-quasi-metric on X is called a quasi-metric space. Note that if q is a quasi-metric on X, then q−1 : X × X → [0,∞) defined by q−1(x,y) = q(y,x) whenever x,y ∈ X is also a quasi- pseudometric on X, called the conjugate quasi-pseudometric of q. As usual, a quasi-pseudometric d on X such that q = q−1 is called a pseudometric on X. keywords: metric; quasi cache: agt-7997.pdf plain text: agt-7997.txt item: #423 of 431 id: agt-8843 author: Das, Pramod; Das, Tarun title: A note on measure and expansiveness on uniform spaces date: 2019-04-01 words: 6808 flesch: 79 summary: Keywords: expansiveness; measure expansiveness; expansive measures; equicontinuity; shadowing; specification. Many of these results have been generalized [15] for expansive measures for maps on non-compact, non-metrizable spaces. keywords: measure; space; uniform cache: agt-8843.pdf plain text: agt-8843.txt item: #424 of 431 id: agt-8981 author: Lazaar, Sami; Nacib, Saber title: The hull orthogonal of the unit inteval [0,1] date: 2018-10-04 words: 3454 flesch: 77 summary: The family of continuous maps rendered invertible by the reflector β ◦ ρ is deduced. On the other hand, in [6], A. Haouati and S. Lazaar showed that the reflective subcategory Hewitt of Top, whose objects are real-compact spaces, is the orthogonal hull of the real line R. Analogous to Sob⊥ = {δ}⊥ and Hewitt⊥ = {R}⊥, we show in this paper that Hcomp⊥ = {I}⊥ where I is the unit interval, and consequently the family of continuous maps rendered invertible by β ◦ ρ are those maps which are orthogonal to I. 2. keywords: orthogonal; space cache: agt-8981.pdf plain text: agt-8981.txt item: #425 of 431 id: agt-9009 author: Megaritis, A.C. title: τ-metrizable spaces date: 2018-10-04 words: 3635 flesch: 82 summary: The mapping ρτ : X × X → R τ + defined by ρτ(x, y) = {ρλ(x, y)}λ∈Λ for every x, y ∈ X is a τ-metric on X. y ∈ X. Let k0 be one fixed element of K. The mapping ρτ′ : X × X → R τ′ + defined by ρτ′(x, y) = {ρ λ τ′(x, y)}λ∈Λ for every x, y ∈ X, where ρλτ′(x, y) = { ρλτ (x, y), if λ ∈ K ρk0τ (x, y), if λ ∈ Λ \ K, is a τ′-metric on X such that Tρ τ ′ = Tρτ . keywords: space cache: agt-9009.pdf plain text: agt-9009.txt item: #426 of 431 id: agt-9058 author: Mehran, S.; Namdari, M.; Soltanpour, S. title: On the essentiality and primeness of λ-super socle of C(X) date: 2018-10-04 words: 3861 flesch: 81 summary: Let X be a λ-discrete space, then the set of λ-essential ideals and the set of free ideals containing Sλ(X) coincide. Let X be a λ-discrete space and E be a free ideal containing Sλ(X), it is well known that every free ideal in C(X) is an essential ideal, see [2, Proposition 2.1] and the comment preceding it, hence E is a λ-essential ideal which implies that the set of λ-essential ideals and the set of free ideals containing Sλ(X) coincide. keywords: c(x; ideal; sλ(x cache: agt-9058.pdf plain text: agt-9058.txt item: #427 of 431 id: agt-9168 author: Kumar, D. Ramesh; Pitchaimani, M. title: Approximation of common fixed points in 2-Banach spaces with applications date: 2019-04-01 words: 5498 flesch: 88 summary: 20, no. 1 (2019), 43-55doi:10.4995/agt.2019.9168 c© AGT, UPV, 2019 Approximation of common fixed points in 2-Banach spaces with applications D. Ramesh Kumar a and M. Pitchaimani b a Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore - 632014, India. (mpitchaimani@yahoo.com) Communicated by E. A. Sánchez-Pérez Abstract The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying gener- alized rational contractive condition in 2-Banach spaces. keywords: fixed; point; − t; − w cache: agt-9168.pdf plain text: agt-9168.txt item: #428 of 431 id: agt-9679 author: Sabao, Hope; Olela Otafudu, Olivier title: Infinite games and quasi-uniform box products date: 2019-04-01 words: 8573 flesch: 80 summary: We then introduce bi-proximal spaces, a concept that gen- eralises proximal spaces to the quasi-uniform setting. However, in this paper we show that the Sorgenfrey line is bi- proximal, which shows that our concept of bi-proximal spaces is more general than that of proximal spaces. keywords: game; proximal; quasi; space cache: agt-9679.pdf plain text: agt-9679.txt item: #429 of 431 id: agt-9737 author: Bonanzinga, Maddalena; Carlson, N.; Cuzzupè, Maria Vittoria; Stavrova, D. title: More on the cardinality of a topological space date: 2018-10-04 words: 5860 flesch: 80 summary: We shall show that C = X. Assume there is y ∈ X \C. For every Bγ1,Bγ2, ...,Bγn−1 ∈ B(y), with |Bγi| > 1∀i = 1,2, ...,n − 1 and γ1,γ2, ...,γn−1 ⊆ µ define Fγ1,γ2,...,γn−1 = {Vc : c ∈ C,Vc ∈ B(c),Vc ∩ Bγ1 ∩ Bγ2 ∩ ... ∩ Bγn−1 = ∅}. Let κ = Uc(X)πχ(X), fix p ∈ X, and let B be a local π-base at p such that |B| ≤ κ. keywords: space cache: agt-9737.pdf plain text: agt-9737.txt item: #430 of 431 id: agt-9943 author: Miller, Alica title: A note about various types of sensitivity in general semiflows date: 2018-10-04 words: 4021 flesch: 79 summary: For any compact subset K of T there exists a compact subset K′ of T such that no translate t + K′, t ∈ T , is contained in K. Another equivalent formulation is the following one. ∈ T , (t + K) ∩A keywords: sensitivity cache: agt-9943.pdf plain text: agt-9943.txt item: #431 of 431 id: agt-9949 author: Dey, Lakshmi Kanta; Kumam, Poom; Senapati, Tanusri title: Fixed point results concerning α-F-contraction mappings in metric spaces date: 2019-04-01 words: 5699 flesch: 86 summary: such that for all x, y ∈ X, d(gx, gy) > 0 The function g is said to be an α-type F-weak contraction if there exists τ > 0 such that for all x, y ∈ X, d(gx, gy) > 0 implies that τ keywords: point cache: agt-9949.pdf plain text: agt-9949.txt