Results 101 to 110 of about 140 (137)
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Annals of Pure and Applied Logic
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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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A Contribution to the Theory of Metrization
Canadian Journal of Mathematics, 1977In a paper on the same subject [28] and another coming out at the same time [27], Nagata gave his celebrated Double (treble, really) Sequence Theorem, with which he deduced easily and thus brought together the basic metrization theorems, i.e. theorems in which the conditions for metrizability are given as the availability of bases or subbases of ...
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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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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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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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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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Metrization of Topological Spaces
Canadian Journal of Mathematics, 1951A single valued function D(x, y) is a metric for a topological space provided that for points x, y, z of the space: 1. the equality holding if and only if x = y, 2. (symmetry), 3. (triangle inequality), 4.
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Summary: Suppose the proximity \(\delta\) is generated by a family \(\Omega\) of entourages of the diagonal. Is then \(\delta\) generated by a uniformity \({\mathcal U}\) of uniform weight \(uw({\mathcal U})\leq\text{Card}(\Omega)\)? In particular, if \(\delta\) is generated by a countable family of entourages is then \(\delta\) metrizable?
Mihaylova, Ekaterina, Nedev, Stoyan
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Mihaylova, Ekaterina, Nedev, Stoyan
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