Results 1 to 10 of about 43 (37)
Electronic Research Archive, 2023 <abstract><p>The present paper aims to investigate some semi-separation axioms relating to the Alexandroff one point compactification (Alexandroff compactification, for short) of the digital plane with the Marcus-Wyse ($ MW $-, for brevity) topology.
Sik Lee, Sang-Eon Han
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On metrization of the hit-or-miss topology using Alexandroff compactification
International Journal of Approximate Reasoning, 2007 The authors consider the hyperspace \(\mathcal F(E)\) of closed subsets of a Hausdorff topological space \(E\), endowed with the so-called Fell topology \(\tau_f\) (termed hit-or-miss topology in the paper) having subbase elements of the form \(\{A\in\mathcal F(E): A\cap U\neq\emptyset\}\) and \(\{A\in\mathcal F(E): A\cap K=\emptyset\}\), where \(U ...
Yangeng Wang
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The Alexandroff one-point compactification as a prototype for extensions
Advances in Mathematics, 2012 As the title suggests, the paper under review deals with extensions of topological spaces, where the extensions are constructed in the spirit of a one point extension, but the remainder can be larger and each point of it ``contributes'' to the extension of the original topology via a suitable ideal. Let \((X,\tau)\) be a topological space, let \((X\cup
Gerald Beer
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Locally compact spaces of countable core and Alexandroff compactification
Topology and Its Applications, 2007 The author introduces a new cardinal invariant, the core of a locally compact \(T_2\)-space (denoted \(cor(X)\)), and states that ``locally compact spaces of countable core generalize locally compact \(\sigma\)-compact spaces in a way that is slightly exotic, but still quite natural''. A subset \(S\) of a locally compact space \(X\) is called saturated
A V Arhangel'Skii
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International Journal of Contemporary Mathematical Sciences, 2016 In the following text we prove that if X is the Alexandroff compactification of a discrete space with at least two elements and f : X → X is a homeomorphism, then in the dynamical system (X, f) the following statements are equivalent: • the dynamical system (X, f) is proximal, 26 Fatemah Ayatollah Zadeh Shirazi et al.
Fatemah Ayatollah Zadeh Shirazi +1 more
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Disconnection in the Alexandroff duplicate
Applied General Topology, 2021 It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space ...
Papiya Bhattacharjee +2 more
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Applied General Topology, 2022 We discuss spaces and the Alexandroff duplicates of those spaces that admit a Č-S embedding into the Čech-Stone compactification of a discrete space.
Andrzej A Szymanski
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Ways of obtaining topological measures on locally compact spaces [PDF]
Известия Иркутского государственного университета: Серия "Математика", 2018 Topological measures and quasi-linear functionals generalize measures and li\-near functionals. Deficient topological measures, in turn, generalize topological measures.
S. V. Butler
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The Fixed Point Property of the Infinite M-Sphere
Mathematics, 2020 The present paper is concerned with the Alexandroff one point compactification of the Marcus-Wyse (M-, for brevity) topological space ( Z 2 , γ ) . This compactification is called the infinite M-topological sphere and denoted by ( ( Z
Sang-Eon Han, Selma Özçağ
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Applied General Topology, 2017 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
Olivier Olela Otafudu, Hope Sabao
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