Applied General Topology - Vol 22, No 1 (2021)
https://riunet.upv.es:443/handle/10251/165208
Sun, 26 Sep 2021 16:39:30 GMT2021-09-26T16:39:30ZApplied General Topology - Vol 22, No 1 (2021)https://riunet.upv.es:443/bitstream/id/882094/
https://riunet.upv.es:443/handle/10251/165208
On the Menger and almost Menger properties in locales
https://riunet.upv.es:443/handle/10251/165253
On the Menger and almost Menger properties in locales
Bayih, Tilahun; Dube, Themba; Ighedo, Oghenetega
[EN] The Menger and the almost Menger properties are extended to locales. Regarding the former, the extension is conservative (meaning that a space is Menger if and only if it is Menger as a locale), and the latter is conservative for sober TD-spaces. Non-spatial Menger (and hence almost Menger) locales do exist, so that the extensions genuinely transcend the topological notions. We also consider projectively Menger locales, and show that, as in spaces, a locale is Menger precisely when it is Lindelöf and projectively Menger. Transference of these properties along localic maps (via direct image or pullback) is considered.
Fri, 16 Apr 2021 09:22:29 GMThttps://riunet.upv.es:443/handle/10251/1652532021-04-16T09:22:29ZDuality of locally quasi-convex convergence groups
https://riunet.upv.es:443/handle/10251/165252
Duality of locally quasi-convex convergence groups
Sharma, Pranav
[EN] In the realm of the convergence spaces, the generalisation of topological groups is the convergence groups, and the corresponding extension of the Pontryagin duality is the continuous duality. We prove that local quasi-convexity is a necessary condition for a convergence group to be c-reflexive. Further, we prove that every character group of a convergence group is locally quasi-convex.
Fri, 16 Apr 2021 09:17:09 GMThttps://riunet.upv.es:443/handle/10251/1652522021-04-16T09:17:09ZDigital homotopic distance between digital functions
https://riunet.upv.es:443/handle/10251/165251
Digital homotopic distance between digital functions
Borat, Ayse
[EN] In this paper, we define digital homotopic distance and give its relation with LS category of a digital function and of a digital image. Moreover, we introduce some properties of digital homotopic distance such as being digitally homotopy invariance.
Fri, 16 Apr 2021 09:14:40 GMThttps://riunet.upv.es:443/handle/10251/1652512021-04-16T09:14:40ZMetric spaces related to Abelian groups
https://riunet.upv.es:443/handle/10251/165250
Metric spaces related to Abelian groups
Veisi, Amir; Delbaznasab, Ali
[EN] When working with a metric space, we are dealing with the additive group (R, +). Replacing (R, +) with an Abelian group (G, ∗), offers a new structure of a metric space. We call it a G-metric space and the induced topology is called the G-metric topology. In this paper, we are studying G-metric spaces based on L-groups (i.e., partially ordered groups which are lattices). Some results in G-metric spaces are obtained. The G-metric topology is defined which is further studied for its topological properties. We prove that if G is a densely ordered group or an infinite cyclic group, then every G-metric space is Hausdorff. It is shown that if G is a Dedekind-complete densely ordered group, (X, d) a G-metric space, A ⊆ X and d is bounded, then f : X → G with f(x) = d(x, A) := inf{d(x, a) : a ∈ A} is continuous and further x ∈ clXA if and only if f(x) = e (the identity element in G). Moreover, we show that if G is a densely ordered group and further a closed subset of R, K(X) is the family of nonempty compact subsets of X, e < g ∈ G and d is bounded, then d′ (A, B) < g if and only if A ⊆ Nd(B, g) and B ⊆ Nd(A, g), where Nd(A, g) = {x ∈ X : d(x, A) < g}, dB(A) = sup{d(a, B) : a ∈ A} and d′ (A, B) = sup{dA(B), dB(A)}.
Fri, 16 Apr 2021 09:11:44 GMThttps://riunet.upv.es:443/handle/10251/1652502021-04-16T09:11:44ZOn sheaves of Abelian groups and universality
https://riunet.upv.es:443/handle/10251/165248
On sheaves of Abelian groups and universality
Iliadis, S.D.; Sadovnichy, Yu. V.
[EN] Universal elements are one of the most essential parts in research fields, investigating if there exist (or not) universal elements in different classes of objects. For example, classes of spaces and frames have been studied under the prism of this universality property. In this paper, studying classes of sheaves of Abelian groups, we construct proper universal elements for these classes, giving a positive answer to the existence of such elements in these classes.
Fri, 16 Apr 2021 09:08:58 GMThttps://riunet.upv.es:443/handle/10251/1652482021-04-16T09:08:58ZRemarks on the rings of functions which have a finite numb er of di scontinuities
https://riunet.upv.es:443/handle/10251/165247
Remarks on the rings of functions which have a finite numb er of di scontinuities
Ahmadi Zand, Mohammad Reza; Khosravi, Zahra
[EN] Let X be an arbitrary topological space. F(X) denotes the set of all real-valued functions on X and C(X)F denotes the set of all f ∈ F(X) such that f is discontinuous at most on a finite set. It is proved that if r is a positive real number, then for any f ∈ C(X)F which is not a unit of C(X)F there exists g ∈ C(X)F such that g ≠ 1 and f = gr f. We show that every member of C(X)F is continuous on a dense open subset of X if and only if every non-isolated point of X is nowhere dense. It is shown that C(X)F is an Artinian ring if and only if the space X is finite. We also provide examples to illustrate the results presented herein.
Fri, 16 Apr 2021 09:06:17 GMThttps://riunet.upv.es:443/handle/10251/1652472021-04-16T09:06:17ZConvexity and freezing sets in digital topology
https://riunet.upv.es:443/handle/10251/165246
Convexity and freezing sets in digital topology
Boxer, Laurence
[EN] We continue the study of freezing sets in digital topology, introduced in [4]. We show how to find a minimal freezing set for a "thick" convex disk X in the digital plane Z^2. We give examples showing the significance of the assumption that X is convex.
Fri, 16 Apr 2021 09:02:33 GMThttps://riunet.upv.es:443/handle/10251/1652462021-04-16T09:02:33ZFrom interpolative contractive mappings to generalized Ciric-quasi contraction mappings
https://riunet.upv.es:443/handle/10251/165245
From interpolative contractive mappings to generalized Ciric-quasi contraction mappings
Roy, Kushal; Panja, Sayantan
[EN] In this article we consider a restricted version of Ciric-quasi contraction mapping for showing that this mapping generalizes several known interpolative type contractive mappings. Also here we introduce the concept of interpolative strictly contractive type mapping T and prove a fixed point theorem for such mapping over a T-orbitally compact metric space. Some examples are given in support of our established results. Finally we give an observation regarding (λ, α, β)-interpolative Kannan contractions introduced by Gaba et al.
Fri, 16 Apr 2021 08:59:45 GMThttps://riunet.upv.es:443/handle/10251/1652452021-04-16T08:59:45ZConvexity and boundedness relaxation for fixed point theorems in modular spaces
https://riunet.upv.es:443/handle/10251/165243
Convexity and boundedness relaxation for fixed point theorems in modular spaces
Lael, Fatemeh; Shabanian, Samira
[EN] Although fixed point theorems in modular spaces have remarkably applied to a wide variety of mathematical problems, these theorems strongly depend on some assumptions which often do not hold in practice or can lead to their reformulations as particular problems in normed vector spaces. A recent trend of research has been dedicated to studying the fundamentals of fixed point theorems and relaxing their assumptions with the ambition of pushing the boundaries of fixed point theory in modular spaces further. In this paper, we focus on convexity and boundedness of modulars in fixed point results taken from the literature for contractive correspondence and single-valued mappings. To relax these two assumptions, we seek to identify the ties between modular and b-metric spaces. Afterwards we present an application to a particular form of integral inclusions to support our generalized version of Nadler’s theorem in modular spaces.
Fri, 16 Apr 2021 08:55:22 GMThttps://riunet.upv.es:443/handle/10251/1652432021-04-16T08:55:22ZIdeal spaces
https://riunet.upv.es:443/handle/10251/165241
Ideal spaces
Mitra, Biswajit; Chowdhury, Debojyoti
[EN] Let C∞ (X) denote the family of real-valued continuous functions which vanish at infinity in the sense that {x ∈ X : |f(x)| ≥ 1/n} is compact in X for all n ∈ N. It is not in general true that C∞ (X) is an ideal of C(X). We define those spaces X to be ideal space where C∞ (X) is an ideal of C(X). We have proved that nearly pseudocompact spaces are ideal spaces. For the converse, we introduced a property called “RCC” property and showed that an ideal space X is nearly pseudocompact if and only if X satisfies ”RCC” property. We further discussed some topological properties of ideal spaces.
Fri, 16 Apr 2021 07:27:52 GMThttps://riunet.upv.es:443/handle/10251/1652412021-04-16T07:27:52Z