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Applied General Topology
Scopus
ISSN 1576-9402 · Universitat Politècnica de València · 676 artikel di indeks
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Artikel Jurnal
The space of decompositions of a continuum
We study the space D(X) of ordered decompositions of a continuum X as a subspace of C(X)2 under the Vietoris topology. Our focus is on the number of components and arc components of D(X). The space D(X) is locally connected and locally compact but never compact unless it is empty. For X irreducible…
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Artikel Jurnal
Novel perturbed b-metric and perturbed extended b-metricspaces with Banach-type fixed point theorem
In this paper, we introduce a new general framework, called perturbed extended b-metric spaces, denoted by (X, D ζ , ℏ) , which extends the classical and extended $b$-metric structures through the inclusion of an explicit perturbation mapping ℏ. This formulation is motivated by the observation that…
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Artikel Jurnal
A topology on the poset of quiver mutation classes
To better understand mutation-invariant and hereditary properties of quivers (and more generally skew-symmetrizable matrices), we have constructed a topology on the set of all mutation classes of quivers which we call the mutation class topology. This topology is the Alexandrov topology induced by…
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Artikel Jurnal
Compactifications of bundles of C*-algebras
This article presents the construction of a bundle of C*-algebras with a compact base space by means of localization processes resorting to inductive limits. This construction achieved in terms of the Stone-Čech compactification provides a solution to the compactness issue raised by P. Bertozzini…
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Artikel Jurnal
Crossconvergence: A new bounded topological presentation
We present crossconvergence, which commonly generalize bornology, preuniform convergence, orderconvergence, b-uniform filtration and grill-determined prenearness. The corresponding construct CCONV forms a strong topological universe, respectively quasitopos, in which quotients are stable under…
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Artikel Jurnal
R-F-spaces and subrings of C(X)
A topological space X is said to be an F-space if the ring C(X), the algebra of all real-valued continuous functions on X, is a Bézout ring (i.e., every finitely generated ideal in C(X) is principal). This is a classical concept in the context of C(X), and various generalizations of this notion…
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Artikel Jurnal
Simple polynomial equations over (m x m)-matrices
Let m be any integer ≥ 3 . We consider the polynomial equation Xn+an-1·Xn-1+···+a1·X+a0·I=O, over (m x m)-matrices X with the real entries, where I is the identity matrix, O is the null matrix, ai ∈ ℝ for each i and n ≥ 1. We discuss its solution set S supplied with the natural Euclidean topology…
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Artikel Jurnal
Symmetric power functors in the category of fuzzy compact spaces
In this paper, we establish that inverse limits of fuzzy compact spaces remain fuzzy compact, using a direct proof based solely on Lowen’s definitions. This result enables a categorical treatment of compactness analogous to the Tychonoff theorem in the classical setting. Moreover, we prove that the…
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Artikel Jurnal
Cellular-P spaces for some Lindelöf-type properties
In this paper, we study two classes of topological spaces: cellular-almost Lindelöf spaces and cellular-weakly Lindelöf spaces. We prove that the classes of cellular-Lindelöf, cellular weakly Lindelöf and cellular-almost Lindelöf are distinct. In addition, we present a comparative study of these…
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Artikel Jurnal
On some convergence approach structures on hyperspaces
In the context of the category Cap of convergence approach spaces and contractions, we introduce and study approach analogs of the upper and lower Kuratowski convergences, upper-Fell and Fell topologies on the set of closed subsets of the coreflection on the category Conv of convergence spaces of a…
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Artikel Jurnal
Interpolative results for cyclic multivalued and Perov type contractions
The aim of this paper is to obtain fixed point results for interpolative Kannan type contraction mappings. The purpose of this paper is two fold: one relates to the fixed point results for multivalued cyclic interpolative Kannan type contractions, and second deals with proving the Perov fixed point…
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Artikel Jurnal
Oscillation and modulus of continuity in uniform spaces
The present paper introduces oscillation and modulus of continuity for functions on uniform spaces. Classical results are established in this framework. Characterizations of continuity and uniform continuity are provided in terms of oscillation and modulus of continuity. Connection functions are…
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Artikel Jurnal
On regular covers at subsets
In this paper, we introduce and investigate the notions of cs-regular, sn-regular, so-regular, and regular families at arbitrary subsets of topological spaces. We study their relationships with point-2-star, cs-star, sn-star, so-star, and o-star networks, as well as with cs-metrizable spaces and…
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Artikel Jurnal
Topological well-orderedness for root-cause identification in networks: canonical explanations via upper-bound graphs
We introduce topological well-orderedness (TWO) for triples ( X , T , ≤ ) , requiring that every nonempty open set admits a least element. For each open set U, we define the upper-bound graph UB(U) by joining x , y ∈ U whenever they share an upper bound in U, and study its clique complex together…
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Artikel Jurnal
Interplay between various graphs on C(X)ρ
This article focuses on the study of zero-divisor graph Γ(C(X)P), annihilator graph AG(C(X)P) and weakly zero-divisor graph WΓ(C(X)P) on the ring C(X)P of all real-valued functions on a topological space X that are continuous outside a member of an ideal P of closed subsets of X. We establish that…
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Artikel Jurnal
Polynomial entropy on regular curves
We show that the polynomial entropy of homeomorphisms on regular curves is bounded above by one. Moreover, the polynomial entropy equals one under the fairly mild condition that the homeomorphism possesses a wandering point. We obtain a rigidity result for homeomorphisms on local dendrites (and…
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Artikel Jurnal
The Hartman-Mycielski construction and topological monomorphisms
Semitopological groups G and H are said to be HM-equivalent if the Hartman-Mycielski extensions G· and H· of G and H, respectively, are topologically isomorphic. It is shown that G and Gk are HM-equivalent, for every semitopological group G and an integer k ≥ 1 . We also show that if G and H are…
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Artikel Jurnal
Development of a robust iterative algorithm for contractive-like mapping in hyperbolic space: application to computational fractal imaging of polynomiographs
The primary objective is to establish the fixed-point convergence analysis of our newly proposed iteration process, within the framework of hyperbolic spaces, particularly in the presence of contractive-like mapping and further investigate its stability characteristics. To demonstrate its…
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Artikel Jurnal
A groupoid approach to the study of fuzzy topological spaces
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of an open subset is closed. To tackle this inconsistency, we…
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Artikel Jurnal
On the extension of partial metrics and quasi-metrics
In a recent article, V. Mykhaylyuk and V. Myronyk investigated the problem of extending partial metrics and quasi-metrics. Concretely, they stated, and proved, as a main result that if A is a closed subset of a partially metrizable space (X,τ) then every compatible partial metric p on A whose…