منابع مشابه
- Metrizable Spaces and Their Applications
In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...
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For every cardinal τ and every ordinal α, we construct a metrizable space Mα(τ) and a strongly countable-dimensional compact space Zα(τ) of weight τ such that D(Mα(τ)) ≤ α, D(Zα(τ)) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of Mα(τ) and to a subspace of Zα+1(τ).
متن کاملUniform Properties and Hyperspaces of Metrizable Spaces
Two equivalent metrics can be compared, with respect to their uniform properties, in several different ways. We present some of them, and then use one of these conditions to characterize which metrics on a space induce the same lower Hausdorff topology on the hyperspace. Finally, we focus our attention to complete metrics.
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We continue Mizar formalization of general topology according to the book [16] by Engelking. In the article, we present the final theorem of Section 4.1. Namely, the paper includes the formalization of theorems on the correspondence between the cardinalities of the basis and of some open subcover, and a discreet (closed) subspaces, and the weight of that metrizable topological space. We also de...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1970
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-66-1-85-93