Results 91 to 100 of about 140 (137)
On metrizability of $M$-spaces
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1964 openaire +2 more sources
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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
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Berestovskii, V. N., Gichev, V. M.
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Berestovskii, V. N., Gichev, V. M.
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Mathematical Logic Quarterly, 2007
AbstractEvery second‐countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space (X, d) can be considered computationally as a subspace of some computable metric space [
Tanja Grubba +2 more
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AbstractEvery second‐countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space (X, d) can be considered computationally as a subspace of some computable metric space [
Tanja Grubba +2 more
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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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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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On Unions of Metrizable Subspaces
Canadian Journal of Mathematics, 1980In this paper we study the question “which generalized metric spaces can be written as the union of k (closed) metrizable subspaces, where k is a cardinal number with k ≤ c?“ Questions of this type first arose in [16] where J. Nagata asked for examples of certain generalized metric spaces which could not be written as the union of countably many closed
van Douwen, Eric K. +3 more
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Metrization of Symmetric Spaces
Canadian Journal of Mathematics, 1975A distance function d on a set X is a function X × X → [0, ∞ ) satisfying (1) d(x, y) = 0 if and only if x = y, and (2) d(x, y) = d(y, x). Such a function determines a topology T on X by agreeing that U is an open set if it contains an ∈-sphere N(p; ∈)( = {x: d(p, x) < ∈﹜} about each of its points.
Harley, P. W. III, Faulkner, G. D.
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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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