Difference between revisions of "Covering"

Latest revision as of 15:15, 2 December 2015

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Now [[covering]] can be used, rather than the longer [[cover|covering]]

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+#REDIRECT [[Cover]]
 ==Definition==
-A covering of a set {{m|A}} is a collection {{m|\mathcal{A} }} where <mm>A\subseteq\bigcup_{S\in\mathcal{A}}S</mm>, that is as you'd expect, a collection of sets which contain {{m|A}} in their union.
+Now {{C|<nowiki>[[covering]]</nowiki>}} can be used, rather than the longer {{C|<nowiki>[[cover|covering]]</nowiki>}}
-==Alternative statement==
+{{Definition|Topology|Metric Space}}
-Munkres seems to go a different route and only lets one cover entire [[Topological space|spaces]], not sets within it. However he shows that considering any set as a [[Subspace topology|subspace]] of {{m|X}} we can then cover it using (open, as it is brought up studying compactness) sets in the ambient space.
-This is mentioned, discussed and proven on the [[Compactness|compactness]] page.
-{{Definition|Topology}}