Congruences on topological spaces with an application to radical theory
Sign Up to like & getrecommendations! Published in 2019 at "Algebra universalis"
DOI: 10.1007/s00012-019-0598-0
Abstract: A congruence is defined on a topological space. This leads to the topological versions of the algebraic isomorphism theorems and some of their consequences. In addition, a Hoehnke radical of a topological space is defined… read more here.
Keywords: congruences topological; theory; application radical; spaces application ... See more keywords
Local properties of topological spaces and remainders in compactifications
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-019-00947-0
Abstract: What can we say about the properties of remainders of spaces which have a certain property $$\mathcal{P}$$ locally? Below, a rather general approach to this question is developed. In particular, we consider remainders of locally… read more here.
Keywords: properties topological; spaces remainders; locally metrizable; local properties ... See more keywords
Variational principles on topological spaces
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DOI: 10.1080/02331934.2019.1671384
Abstract: To the best of our knowledge, all the existing variational principles were established in the framework of a complete metric space or a Banach space. In this paper, we consider variational principles in topological spaces.… read more here.
Keywords: topological spaces; principles topological; space; variational principles ... See more keywords
On a new convergence in topological spaces
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DOI: 10.1515/math-2019-0123
Abstract: Abstract In this paper, we introduce a new way-below relation in T0 topological spaces based on cuts and give the concepts of SI2-continuous spaces and weakly irreducible topologies. It is proved that a space is… read more here.
Keywords: topological spaces; si2 continuous; topology; convergence topological ... See more keywords
Vector optimization problems with weakened convex and weakened affine constraints in linear topological spaces
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DOI: 10.1515/math-2024-0073
Abstract: Abstract In this article, we work on vector optimization problems in linear topological spaces. Our vector optimization problems have weakened convex inequality constraints and weakened affine equality constraints. Our inequalities are given by partial orders… read more here.
Keywords: linear topological; topological spaces; vector optimization; optimization problems ... See more keywords
On structural numbers of topological spaces
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DOI: 10.1515/ms-2025-0090
Abstract: Abstract Zero-dimensional structural numbers Z0ind and Z0dim $\mathcal{Z}_0^{\text {ind }} \text { and } \mathcal{Z}_0^{\text {dim }}$ w.r.t. dimensions ind and dim were introduced by Georgiou, Hattori, Megaritis, and Sereti. Somewhat similarly, we define structural numbers Sn𝒜… read more here.
Keywords: numbers topological; topological spaces; dim; structural numbers ... See more keywords
γ-operation & decomposition of some forms of fuzzy soft mappings on fuzzy soft ideal topological spaces
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DOI: 10.2298/fil2001187e
Abstract: In this paper, we extend the notion of γ−operation by using the fuzzy soft ideal notions. Furthermore, we introduce some forms of fuzzy soft continuity in fuzzy soft topological spaces via fuzzy soft ideals. The… read more here.
Keywords: forms fuzzy; topological spaces; soft ideal; decomposition forms ... See more keywords
Reversibility of Tk-topological spaces and the universality problem for the collection of Tk-topological spaces
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DOI: 10.2298/fil2505585l
Abstract: As a generalization of the Khalimsky line topological space, consider the topological space (Z, Tk) (resp. (Z, T?k)) on the set of integers, where the topology Tk (resp. T?k) is generated by the set Sk… read more here.
Keywords: topological space; topological spaces; problem; space ... See more keywords
Quantale-valued generalizations of approach spaces and quantale-valued topological spaces
Sign Up to like & getrecommendations! Published in 2019 at "Quaestiones Mathematicae"
DOI: 10.2989/16073606.2018.1516250
Abstract: Abstract We show that for certain quantales, the categories of quantale-valued gauge spaces and of quantale-valued approach system spaces are isomorphic to the category of quantale-valued bounded strong topological spaces. read more here.
Keywords: spaces quantale; generalizations approach; topological spaces; valued generalizations ... See more keywords
On the Structure of Topological Spaces
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DOI: 10.3390/axioms11020049
Abstract: The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spatial. A… read more here.
Keywords: structure topological; fibrous preorders; topological spaces; structure ... See more keywords
Bounded Sets in Topological Spaces
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DOI: 10.3390/axioms11020071
Abstract: Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is… read more here.
Keywords: topological spaces; space; sets topological; bounded sets ... See more keywords