Results 141 to 150 of about 307 (168)
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Metrizable and weakly metrizable coset spaces
Topology and its Applications, 2021Metrization theorems play an essential role in general topology and analysis. The classical Birkhoff-Kakutani Theorem states that a topological group \(G\) is metrizable if and only if it is \(T_1\) and first-countable. The condition of being first-countable can be weakened with some additional properties which hold automatically for first-countable ...
Ling, Xuewei, Lin, Shou, He, Wei
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Journal of Mathematical Sciences, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berestovskii, V. N., Gichev, V. M.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Berestovskii, V. N., Gichev, V. M.
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Strongly $��$-metrizable spaces are super $��$-metrizable
20162 ...
Lin, Fucai, Lin, Shou
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Metrizable and 2-Metrizable Topological Spaces
Journal of Dynamical Systems and Geometric Theories, 2012Abstract In this paper we introduce (∈ − 2)-ball centered at each point in 2-metric topological space (X,d). Theorems on the normal, regular and Hausdorff topological spaces in 2-metrizable topological space are presented. We show that every metrizable topological spaces are coarser than 2-metrizable topological space, and then we conclude that each ...
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Metrizability and Coconnectedness
Applied Categorical Structures, 2006A topological space \(X\) is called coconnected if every continuous map \(f:X^2\to X\) depends on at most one coordinate. Solving a problem stated in \textit{J. Sichler} and \textit{V. Trnková} [Topology Appl. 142, No. 1--3, 159--179 (2004; Zbl 1068.54009)], the author constructs metric spaces \(X=(P,\mu)\) and \(Y=(P,\nu)\) such that the four monoids \
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Mathematische Nachrichten, 1970
A pseudobase for a topological space \(X\) is a family \(\mathcal P\) of subsets of \(X\) such that if \(C\subset U\), with \(C\) compact and \(U\) open in \(X\), then there is a finite subfamily \(\{P_i\}\subset \mathcal P\) such that \(C\subset \cup P_i\subset U\). The members of \(\mathcal P\) are not necessarily open.
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A pseudobase for a topological space \(X\) is a family \(\mathcal P\) of subsets of \(X\) such that if \(C\subset U\), with \(C\) compact and \(U\) open in \(X\), then there is a finite subfamily \(\{P_i\}\subset \mathcal P\) such that \(C\subset \cup P_i\subset U\). The members of \(\mathcal P\) are not necessarily open.
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2013
The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complet, detailed proofs, and a large number of examples and counterexamples are provided.
Mitrea, Dorina +3 more
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The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complet, detailed proofs, and a large number of examples and counterexamples are provided.
Mitrea, Dorina +3 more
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Alternative Metrization Proofs
Canadian Journal of Mathematics, 1966Alternative methods of proving several classical metrization theorems are offered in this paper, showing that they follow by elementary methods from an early theorem of Alexandroff and Urysohn. A simplified proof of the latter theorem is also given. Theorem 5 and a corollary to Theorem 3 state the main results.
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Non-Metrizable Uniformities and Proximities on Metrizable Spaces
Canadian Journal of Mathematics, 1973In the literature there exist examples of metrizable spaces admitting nonmetrizable uniformities (e.g., see [3, Problem C, p. 204]). In this paper, this phenomenon is presented more coherently by showing that every non-compact metrizable space admits at least one non-metrizable proximity and uncountably many non-metrizable uniformities.
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Canadian Mathematical Bulletin, 1984
AbstractK. Kunugi introduced the notion of ranked space as a generalization of that of metric spaces, (see [6]). In this note we define a metrizability of ranked spaces and study conditions under which a ranked space is metrizable.
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AbstractK. Kunugi introduced the notion of ranked space as a generalization of that of metric spaces, (see [6]). In this note we define a metrizability of ranked spaces and study conditions under which a ranked space is metrizable.
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