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Transcript
properties of compact spaces∗ rspuzio† 2013-03-21 15:35:16 We list the following commonly quoted properties of compact topological spaces. • A closed subset of a compact space is compact • A compact subspace of a Hausdorff space is closed • The continuous image of a compact space is compact • Compactness is equivalent to sequential compactness in the metric topology ∗ hPropertiesOfCompactSpacesi created: h2013-03-21i by: hrspuzioi version: h33966i Privacy setting: h1i hResulti h54D30i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1
