Applied General Topology - Vol 24, No 1 (2023)
https://riunet.upv.es:443/handle/10251/192965
Mon, 09 Sep 2024 07:24:07 GMT2024-09-09T07:24:07ZApplied General Topology - Vol 24, No 1 (2023)https://riunet.upv.es:443/bitstream/id/1040137/
https://riunet.upv.es:443/handle/10251/192965
Common fixed point results for a generalized ( ψ, φ )-rational contraction
https://riunet.upv.es:443/handle/10251/193029
Common fixed point results for a generalized ( ψ, φ )-rational contraction
Arya, Mahesh Chandra; Chandra, N.; Joshi, Mahesh C.
[EN] In this paper, we obtain two common fixed point results for mappings satisfying the generalized (ψ,φ)-contractive type conditions given by a rational expression on a complete metric space. Our results generalize several well known theorems of the literature in the context of (ψ,φ)-rational contraction. In addition, there is an example for obtained results.
Tue, 02 May 2023 07:11:07 GMThttps://riunet.upv.es:443/handle/10251/1930292023-05-02T07:11:07ZΤ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion
https://riunet.upv.es:443/handle/10251/193028
Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion
Jäger, Gunther
[EN] Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces.
Tue, 02 May 2023 07:07:38 GMThttps://riunet.upv.es:443/handle/10251/1930282023-05-02T07:07:38ZNew results regarding the lattice of uniform topologies on C(X)
https://riunet.upv.es:443/handle/10251/193027
New results regarding the lattice of uniform topologies on C(X)
Pichardo-Mendoza, Roberto; Ríos-Herrejón, Alejandro
[EN] For a Tychonoff space X, the lattice UX was introduced in L. A. Pérez-Morales, G. Delgadillo-Piñón, and R. Pichardo-Mendoza, The lattice of uniform topologies on C(X), Questions and Answers in General Topology 39 (2021), 65-71.
In the present paper we continue the study of UX. To be specific, the present paper deals, in its first half, with structural and categorical properties of UX, while in its second part focuses on cardinal characteristics of the lattice and how these relate to some cardinal functions of the space X.
Tue, 02 May 2023 07:01:23 GMThttps://riunet.upv.es:443/handle/10251/1930272023-05-02T07:01:23ZInterpolative contractions and discontinuity at fixed point
https://riunet.upv.es:443/handle/10251/193026
Interpolative contractions and discontinuity at fixed point
Taş, Nihal
[EN] In this paper, we investigate new solutions to the Rhoades’ discontinuity problem on the existence of a self-mapping which has a fixed point but is not continuous at the fixed point on metric spaces. To do this, we use the number defined as n(x,y)=[d(x,y)]β[d(x,Ty)]α[d(x,Ty)]γ[(d(x,Ty)+d(x,Ty))/2]1−α−β−γ, where α , β , γ ∈ ( 0,1 ) with α + β + γ < 1 and some interpolative type contractive conditions. Also, we investigate some geometric properties of Fix(T) under some interpolative type contractions and prove some fixed-disc (resp. fixed-circle) results. Finally, we present a new application to the discontinuous activation functions.
Tue, 02 May 2023 06:56:05 GMThttps://riunet.upv.es:443/handle/10251/1930262023-05-02T06:56:05ZSome network-type properties of the space of G-permutation degree
https://riunet.upv.es:443/handle/10251/193025
Some network-type properties of the space of G-permutation degree
Kočinac, Ljubisa D.R; Mukhamadiev, F. G.; Sadullaev, A. K.; Meyliev, Sh. U.
[EN] In this paper the network-type properties (network, cs−network, cs∗−network, cn−network and ck−network) of the space SPn GX of Gpermutation degree of X are studied. It is proved that: (1) If X is a T1-space that has a network of cardinality ≤ κ, then SPn GX has a network of cardinality ≤ κ; (2) If X is a T1-space that has a cs-network (resp. cs∗-network) of cardinality ≤ κ, then SPn GX has a cs-network (resp. cs∗-network) of cardinality ≤ κ; (3) If X is a T1-space that has a cn-network (resp. ck-network) of cardinality ≤ κ, then SPn
GX has a cn-network (resp. ck−network) of cardinality ≤ κ.
Tue, 02 May 2023 06:47:36 GMThttps://riunet.upv.es:443/handle/10251/1930252023-05-02T06:47:36ZHybrid topologies on the real line
https://riunet.upv.es:443/handle/10251/193024
Hybrid topologies on the real line
Richmond, Tom
[EN] Given A ⊆ R, the Hattori space H(A) is the topological space (R, τA) where each a ∈ A has a τA-neighborhood base {(a−ε, a+ε) : ε > 0} and each b ∈ R − A has a τA-neighborhood base {[b, b + ε) : ε > 0}. Thus, τA may be viewed as a hybrid of the Euclidean topology and the lowerlimit topology. We investigate properties of Hattori spaces as well as other hybrid topologies on R using various combinations of the discrete, left-ray, lower-limit, upper-limit, and Euclidean topologies. Since each of these topologies is generated by a quasi-metric on R, we investigate hybrid quasi-metrics which generate these hybrid topologies.
Tue, 02 May 2023 06:43:27 GMThttps://riunet.upv.es:443/handle/10251/1930242023-05-02T06:43:27ZA counter example on a Borsuk conjecture
https://riunet.upv.es:443/handle/10251/193023
A counter example on a Borsuk conjecture
Cholaquidis, Alejandro
[EN] The study of shape restrictions of subsets of Rd has several applications in many areas, being convexity, r-convexity, and positive reach, some of the most famous, and typically imposed in set estimation. The following problem was attributed to K. Borsuk, by J. Perkal in 1956: find an r-convex set which is not locally contractible. Stated in that way is trivial to find such a set. However, if we ask the set to be equal to the closure of its interior (a condition fulfilled for instance if the set is the support of a probability distribution absolutely continuous with respect to the d-dimensional Lebesgue measure), the problem is much more difficult. We present a counter example of a not locally contractible set, which is r-convex. This also proves that the class of supports with positive reach of absolutely continuous distributions includes strictly the class ofr-convex supports of absolutely continuous distributions.
Tue, 02 May 2023 06:40:13 GMThttps://riunet.upv.es:443/handle/10251/1930232023-05-02T06:40:13ZProper spaces are spectral
https://riunet.upv.es:443/handle/10251/193022
Proper spaces are spectral
Goswami, Amartya
[EN] Since Hochster's work, spectral spaces have attracted increasing interest. Through this note we give a new self-contained and constructible topology-independent proof of the fact that the set of proper ideals of a ring endowed with coarse lower topology is a spectral space.
Tue, 02 May 2023 06:35:57 GMThttps://riunet.upv.es:443/handle/10251/1930222023-05-02T06:35:57ZBest proximity point for q-ordered proximal contraction in noncommutative Banach spaces
https://riunet.upv.es:443/handle/10251/193021
Best proximity point for q-ordered proximal contraction in noncommutative Banach spaces
Bartwal, Ayush; Rawat, Shivam; Beg, Ismat
[EN] We introduce the concept of q-ordered proximal nonunique contraction for the non self mappings and then obtain some proximity point results for these mappings. We also furnish examples to support our claims.
Tue, 02 May 2023 06:20:39 GMThttps://riunet.upv.es:443/handle/10251/1930212023-05-02T06:20:39ZC(X) determines X - an inherent theory
https://riunet.upv.es:443/handle/10251/193020
C(X) determines X - an inherent theory
Mitra, Biswajit; Das, Sanjib
[EN] One of the fundamental problem in rings of continuous function is to extract those spaces for which C(X) determines X, that is to investigate X and Y such that C(X) isomorphic with C(Y ) implies X homeomorphic with Y. The development started back from Tychonoff who first pointed out inevitability of Tychonoff space in this category of problem. Later S. Banach and M. Stone proved independently with slight variance, that if X is compact Hausdorff space, C(X) also determine X. Their works were maximally extended by E. Hewitt by introducing realcompact spaces and later Melvin Henriksen and Biswajit Mitra solved the problem for locally compact and nearly realcompact spaces. In this paper we tried to develop an inherent theory of this problem to cover up all the works in the literature introducing a notion so called P-compact spaces.
Tue, 02 May 2023 06:18:53 GMThttps://riunet.upv.es:443/handle/10251/1930202023-05-02T06:18:53Z