
Bell, Kathleen; Richmond, Tom
[EN] If A(t) and B(t) are subsets of the Euclidean plane which are continuously morphing, we investigate the question of whether they may morph directly from being disjoint to overlapping so that the boundary and interior of A(t) both intersect the boundary and interior of B(t) without first passing through a state in which only their boundaries intersect. More generally, we consider which 4intersection valuesbinary 4tuples specifying whether the boundary and interior of A(t) intersect the boundary and interior of B(t)are adjacent to which in the sense that one may morph into the other without passing through a third value....

Phuengrattana, Withun
[EN] In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a deltaconvergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces.

Olela Otafudu, Olivier; Sabao, Hope
[EN] We revisit the computation of entourage sections of the constant uniformity of the product of countably many copies the Alexandroff onepoint compactification called the Fort space. Furthermore, we define the concept of a quasiuniformity on a product of countably many copies of a quasiuniform space, where the symmetrised uniformity of our quasiuniformity coincides with the constant uniformity. We use the concept of Cauchy filter pairs on a quasiuniform space to discuss the completeness of its quasiuniform box product.

Hattab, Hawete
[EN] Let G be a subgroup of the group Homeo(E) of homeomorphisms of a Hausdorff topological space E. The class of an orbit O of G is the union of all orbits having the same closure as O. We denote by E=eG the space of classes of orbits called quasiorbit space. A space X is called a quasiorbital space if it is homeomorphic to E=eG where E is a compact Hausdorff space. In this paper, we show that every in nite second countable quasicompact T0space is the quotient of a quasiorbital space.

Krebs, Mike
[EN] We show that there exists a Hausdorff topology on the set R of real numbers such that a subset A of R has compact closure if and only if A is countable. More generally, given any set X and any infinite set S, we prove that there exists a Hausdorff topology on X such that a subset A of X has compact closure if and only if the cardinality of A is less than or equal to that of S. When we attempt to replace “than than or equal to” in the preceding statement with “strictly less than,” the...

de la Barrera Mayoral, Daniel
[EN] In this paper we give two families of nonmetrizable topologies on the group of the integers having a countable dual group which is isomorphic to a infinite torsion subgroup of the unit circle in the complex plane. Both families are related to Dsequences, which are sequences of natural numbers such that each term divides the following. The first family consists of locally quasiconvex group topologies. The second consists of complete topologies which are not locally quasiconvex. In order to study the dual groups for both families we need to make numerical considerations of independent interest.

Dost, Senol
[EN] Textures are pointset setting for fuzzy sets, and they provide a framework for the complementfree mathematical concepts. Further dimetric on textures is a gener alization of classical metric spaces. The aim of this paper is to give some properties of dimetric texture space by using categorical approach. We prove that the category of clas sical metric spaces is isomorphic to a full subcategory of dimetric texture spaces, and give a natural transformation from metric topologies to dimetric ditopologies. Further, it is pre sented a relation between dimetric texture spaces and quasipseudo metric spaces in the sense of J. F....

Onsod, Wudthichai; Kumam, Poom; Cho, Yoel Je
[EN] In this paper, by using the concept of the αGaraghty contraction, we introduce the new notion of the αΘGaraghty type contraction and prove some fixed point results for this contraction in partial metric spaces. Also, we give some examples and applications to illustrate the main results.

Mongkolkeha, Chirasak; Cho, Yeol Je; Kumam, Poom
[EN] The purpose of this article is to prove some fixed point theorems for simulation functions in complete bmetric spaces with partially ordered by using wtdistance which introduced by Hussain et al. Also, we give some examples to illustrate our main results.

Boxer, Laurence
[EN] We study properties of shy maps in digital topology.

Bisht, Ravindra K; Pant, R. P.
[EN] In this paper, we investigate some contractive definitions which are strong enough to generate a fixed point that do not force the mapping to be continuous at the fixed point. Finally, we obtain a fixed point theorem for generalized nonexpansive mappings in metric spaces by employing MeirKeeler type conditions.

Ozturk, Vildan; Ansari, Arslan Hojat
[EN] In this paper, we consider and generalize recent b(E.A)property results in [11] via the concepts of Cclass functions in b metric spaces. A example is given to support the result.

Sultana, Asrifa; Vetrivel, V.
[EN] We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent fixed point and best proximity point results.

Milani, Vida; Mansourbeigi, Seyed M.H.; Finizadeh, Hossein
[EN] In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.

Dube, Themba
[EN] We revisit weak pseudocompactness in pointfree topology, and show that a locale is weakly pseudocompact if and only if it is Gδdense in some compactification. This localic approach (in contrast with the earlier frametheoretic one) enables us to show that finite localic products of locales whose nonvoid Gδsublocales are spatial inherit weak pseudocompactness from the factors. We also show that if a locale is weakly pseudocompact and its Gδsublocales are complemented then it is Baire.

GarcíaMáynez, Adalberto; Pimienta Acosta, Adolfo
[EN] In this paper we prove there is a bijection between the set of all annular bases of a topological spaces $(X,\tau)$ and the set of all transitive quasiproximities on $X$ inducing $\tau$.We establish some properties of those topological spaces $(X,\tau)$ which imply that $\tau$ is the only annular basis

Sari, Dewi Kartika; Zhao, Dongsheng
[EN] Using neighbourhood assignments, we introduce and study a new cardinal function, namely GCI(X), for every topological space X. We shall mainly investigate the spaces X with finite GCI(X). Some properties of this cardinal in connection with special types of mappings are also proved.
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