Results 161 to 170 of about 15,159 (191)
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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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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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Mathematical Notes of the Academy of Sciences of the USSR, 1973
The problem about the necessity of the Doichinov-Nedev condition for the Δ-metrizability of a topological space and the Stoltenberg problem, whether every Moore space is Δ-metrizable, has negative solutions in the class of completely regular topological spaces (see [7]).
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The problem about the necessity of the Doichinov-Nedev condition for the Δ-metrizability of a topological space and the Stoltenberg problem, whether every Moore space is Δ-metrizable, has negative solutions in the class of completely regular topological spaces (see [7]).
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2013
This is a survey of results on generalized metrizable spaces obtained in the past 10 years.
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This is a survey of results on generalized metrizable spaces obtained in the past 10 years.
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Canadian Journal of Mathematics, 1973
An unsolved problem in metrization theory is whether every Hausdorff M-space with a Gg-diagonal is metrizable. There are several recent results which have a bearing upon this question. In [9], P. Zenor showed that an M-space is metrizable if and only if it has a regular Gδ-diagonal; in [1], Borges showed that a regular meta-Lindelöf M-space is ...
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An unsolved problem in metrization theory is whether every Hausdorff M-space with a Gg-diagonal is metrizable. There are several recent results which have a bearing upon this question. In [9], P. Zenor showed that an M-space is metrizable if and only if it has a regular Gδ-diagonal; in [1], Borges showed that a regular meta-Lindelöf M-space is ...
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On Metrizability of Topological Spaces
Canadian Journal of Mathematics, 1968Our present work is divided into three sections. In §2 we study the metrizability of spaces with a Gδ-diagonal (see Definition 2.1). In §3 we study the metrization of topological spaces by means of collections of (not necessarily continuous) real-valued functions on a topological space.
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1995
A topological space,X is compact if every open cover of X has a finite subcover, i.e., if (U i ) i∈I is a family of open sets and X\(X = \bigcup\nolimits_{i \in I} {{U_i}}\), then there is finite \({I_0} \subseteq I\) such that \(X = \bigcup\nolimits_{i \in {I_0}} {{U_i}}\).This is equivalent to saying that every family of closed subsets of X with the ...
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A topological space,X is compact if every open cover of X has a finite subcover, i.e., if (U i ) i∈I is a family of open sets and X\(X = \bigcup\nolimits_{i \in I} {{U_i}}\), then there is finite \({I_0} \subseteq I\) such that \(X = \bigcup\nolimits_{i \in {I_0}} {{U_i}}\).This is equivalent to saying that every family of closed subsets of X with the ...
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Proto-metrizable fuzzy topological spaces
1999In this paper we define for fuzzy topological spaces a notion corresponding to protometrizable topological spaces. We obtain some properties of these fuzzy topological spaces, particularly we give relations with non-archimedean, and metrizable fuzzy topological spaces.
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