Difference between revisions of "Covering"
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Revision as of 05:30, 15 February 2015
Definition
A covering of a set A is a collection A where A⊂∪S∈AS, that is as you'd expect, a collection of sets which contain A in their union.
Alternative statement
Munkres seems to go a different route and only lets one cover entire spaces, not sets within it. However he shows that considering any set as a subspace of 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 page.
