Results 101 to 110 of about 2,673 (127)

Metrized Semigroups

Journal of Mathematical Sciences, 2004
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Berestovskii, V. N., Gichev, V. M.
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Strongly $��$-metrizable spaces are super $��$-metrizable

2016
2 ...
Lin, Fucai, Lin, Shou
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Metrizable and 2-Metrizable Topological Spaces

Journal of Dynamical Systems and Geometric Theories, 2012
Abstract 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, 2006
A 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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A Metrization Theorem

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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Groupoid Metrization Theory

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, Mitrea, Irina, Mitrea, Marius, Monniaux, Sylvie   +3 more
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Alternative Metrization Proofs

Canadian Journal of Mathematics, 1966
Alternative 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, 1973
In 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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Metrization of Ranked Spaces

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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Computable metrization

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, Matthias Schröder, Klaus Weihrauch   +2 more
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