## Recursos de colección

#### RiuNet. Repositorio institucional de la Universitat de Valencia (74.547 recursos)

RiuNet es el Repositorio Institucional de la Universitat Politècnica de València, gestionado por la Biblioteca, cuyo objetivo es ofrecer acceso en Internet a la producción científica, académica y corporativa de la comunidad universitaria con la finalidad de aumentar su visibilidad y hacerla accesible y preservable.

Applied General Topology

1. #### Transitions between 4-intersection values of planar regions

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 4-intersection values---binary 4-tuples 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....

2. #### On the generalized asymptotically nonspreading mappings in convex metric spaces

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 delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces.

3. #### On quasi-uniform box products

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 one-point compactification called the Fort space. Furthermore, we define the concept of a quasi-uniformity on a product of countably many copies of a quasi-uniform space, where the symmetrised uniformity of our quasiuniformity coincides with the constant uniformity. We use the concept of Cauchy filter pairs on a quasi-uniform space to discuss the completeness of its quasi-uniform box product.

4. #### On quasi-orbital space

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 quasi-orbit space. A space X is called a quasi-orbital 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 quasi-compact T0-space is the quotient of a quasi-orbital space.

5. #### On cardinalities and compact closures

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...

6. #### Non metrizable topologies on Z with countable dual group.

de la Barrera Mayoral, Daniel
[EN] In this paper we give two families of non-metrizable 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 D-sequences, which are sequences of natural numbers such that each term divides the following. The first family consists of locally quasi-convex group topologies. The second consists of complete topologies which are not locally quasi-convex. In order to study the dual groups for both families we need to make numerical considerations of independent interest.

7. #### Metric spaces and textures

Dost, Senol
[EN] Textures are point-set setting for fuzzy sets, and they provide a framework for the complement-free 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 quasi-pseudo metric spaces in the sense of J. F....

8. #### Fixed points of α-Θ-Geraghty type and Θ-Geraghty graphic type contractions

Onsod, Wudthichai; Kumam, Poom; Cho, Yoel Je
[EN] In this paper, by using the concept of the α-Garaghty contraction, we introduce the new notion of the α-Θ-Garaghty 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.

9. #### Fixed point theorems for simulation functions in $\mbox{b}$-metric spaces via the $wt$-distance

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 b-metric spaces with partially ordered by using wt-distance which introduced by Hussain et al. Also, we give some examples to illustrate our main results.

10. #### Digital shy maps

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

11. #### Contractive definitions and discontinuity at fixed point

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 Meir-Keeler type conditions.

12. #### Common fixed point theorems for mappings satisfying (E.A)-property via C-class functions in b-metric spaces

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 C-class functions in b- metric spaces. A example is given to support the result.

13. #### Best proximity points of contractive mappings on a metric space with a graph and applications

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.

14. #### Algebraic and topological structures on rational tangles

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.

15. #### A note on weakly pseudocompact locales

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

16. #### A note on unibasic spaces and transitive quasi-proximities

[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 quasi-proximities on $X$ inducing $\tau$.We establish some properties of those topological spaces $(X,\tau)$ which imply that $\tau$ is the only annular basis