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Metrization theorem
This space is Hausdorff, paracompact and first countable. The long line is locally metrizable but not ...
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Topological property - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Topological_property
A space is called Polish if it is metrizable with a separable and complete metric. Locally metrizable. A space is locally metrizable if every point has a metrizable ... |
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Paracompact space - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Paracompact_space
(Smirnov metrization theorem) A topological space is metrizable if and only if it is paracompact, Hausdorff, and locally metrizable. Michael selection theorem ... |
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May 11, 2008 ... Locally metrizable space. From Topospaces. Jump to: navigation, search. This article defines a property of topological spaces: a property that ...
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In a metric space (X, d), a dense set is a subset A ⊂ X such that, for any x ∈ X and any ϵ > 0, there exists y ∈ A, satisfying d(x, y) < ϵ. A local base of a point x ...
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In this paper, we prove that a space X is a locally separable metrizable ... [1] characterized locally separable metrizable spaces by topological sums of separable ...
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Is it possible for a space to be compact, Hausdorff, totally disconnected, first countable, and nowhere locally metrizable? This problem came up ...
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Let X be a locally compact Hausdorff space. Then. X is metrizable ⇐ X is 2nd countable. ⇒: Any discrete uncountable space is metrizable and not 2nd countable.
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Jan 14, 2011 ... The space is too big: examples like the uncountable ordinal and the long line fall under this heading. But they are still locally metrizable, so we ...
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Abstract. With a certain natural topology, the fundamental group of a locally path connected metric space X becomes discrete if and only if X is semilocally simply ...
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