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单词 PropertiesOfCompactSpaces
释义

properties of compact spaces


We list the following commonly quoted properties of compactPlanetmathPlanetmath topological spacesMathworldPlanetmath.

  • A closed subset of a compact space is compact

  • A compact subspaceMathworldPlanetmathPlanetmath of a Hausdorff space is closed

  • The continuousPlanetmathPlanetmath image of a compact space is compact

  • Compactness is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath to sequential compactness in the metric topology

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更新时间:2025/5/4 19:29:46