Metrization theorem
... topology and related areas of mathematics, a metrizable space is a topological space that is ... X,\tau) is said to be metrizable if there is a metric $d\; ...\; conditions\; for\; a\; topological\; space\; to\; be$metrizable. Metrizable spaces inherit all topological properties from metric ... every second-countable regular Hausdorff space is metrizable. So, for example, every second-countable ...
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Topology glossary
... complete if every Cauchy sequence converges. Completely metrizable/completely metrisable. See complete space. Completely normal ... subsets. See also countably locally finite. Locally metrizable/Locally metrisable. A space is locally metrizable if every point has a metrizable neighbourhood. Locally path-connected. A space is ... Tychonoff). Every metric space is first-countable. Metrizable/Metrisable. A space is metrizable if ...
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Topological property
... proper open subset called a monolith. Metrizability Metrizable. A space is metrizable if it is homeomorphic to a metric space. Metrizable spaces are always Hausdorff and paracompact (and ... space is called Polish if it is metrizable with a separable and complete metric. Locally metrizable. A space is locally metrizable if ...
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Glossary of topology   (translated from Spanish)
... if each succession of Cauchy converges. Completely metrizable. To see Complete Topológicamente. Completely normal. A ... a finite number of such subgroups. Locally metrizable. A space is it if each point has metrizable surroundings. Locally connected by ways. A space ... d it is called metric in M. Metrizable. A space is it if he is ... A space says "Polish" if it is metrizable with metric separable and it completes. ...
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Cantor space
... non-empty, perfect, compact, totally disconnected, and metrizable. It is also equivalent (via Stone's ... Cantor set.) Also, every uncountable, separable, completely metrizable space contains Cantor spaces as subspaces. This ... a corollary, we see that separable, completely metrizable spaces satisfy the Continuum hypothesis: Every such ... spaces: A Hausdorff topological space is compact metrizable if and only if it is a ...
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Manifold/old
... locally path-connected, locally compact and locally metrizable. Being locally compact Hausdorff spaces they are ... can be shown that a manifold is metrizable if and only if it is paracompact ... can be shown that a manifold is metrizable if and only if it is paracompact ...
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Category:Previous 168 years   (translated from Chinese)
... spatial □□□□is spatial □. But □metrization(Completely metrizable/completely metrisable). □□ Analysis situs □. Completely ... Locally finite)。 空間的一組子集被稱為局部有限，是指每個點都有個鄰域只和有限個這組子集中的成員相交。參閱 可數局部有限. 局部可度量(Locally metrizable/Locally metrisable)。 如果空間中的每個點都有個由可度量鄰域組成的局部基底，則稱這個空間是局部可度量空間。 局部道路連通(Locally path ... 所以也是正規且 Tychonoff)。 所有的度量空間都是 first-countable。 可度量化(Metrizable/Metrisable)。 一個空間被稱為可度量化，指的是這個空間和某個度量空間同胚。所有的可度量化空間都是 Hausdorff 且 paracompact (所以也是正規且 ...
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Inductive dimension
... Such spaces are exactly the separable and metrizable X (see Urysohn's metrization theorem). The ... spaces of dimension n.) Assuming only X metrizable we have ( Miroslav Katětov ) ind X ≤ ...
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Topological manifold
... locally path-connected, locally compact and locally metrizable. Being locally compact Hausdorff spaces they are ... can be shown that a manifold is metrizable if and only if it is paracompact ...
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Approach space
... on N. In contrast, βN is not metrizable. Equivalent definitions Lowen has offered at least ... One can even "distancize" such badly non-metrizable spaces like βN, the Stone-Čech compactification ...
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