Results 241 to 250 of about 859 (275)
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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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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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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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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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Annals of Pure and Applied Logic
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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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Mathematics of the USSR-Izvestiya, 1980
In this paper the author studies spaces in which one can define a "distance" from points to canonically closed sets (the -metric). It is proved that products of metric spaces and locally compact groups are examples of such spaces, and in these cases the -metric can be constructed so that an analogue of the triangle axiom is satisfied.
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In this paper the author studies spaces in which one can define a "distance" from points to canonically closed sets (the -metric). It is proved that products of metric spaces and locally compact groups are examples of such spaces, and in these cases the -metric can be constructed so that an analogue of the triangle axiom is satisfied.
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Canadian Journal of Mathematics, 1977
Let X be a set. A function d from X X X into the nonnegative real numbers is called a ﹛non-archimedean) quasi-metric on X ...
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Let X be a set. A function d from X X X into the nonnegative real numbers is called a ﹛non-archimedean) quasi-metric on X ...
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