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compact∗
djao†
2013-03-21 12:39:20
A topological space X is compact if, for every collection {Ui }i∈I of open sets
in X whose union is X, there exists a finite subcollection {Uij }nj=1 whose union
is also X.
A subset Y of a topological space X is said to be compact if Y with its
subspace topology is a compact topological space.
Note: Some authors require that a compact topological space be Hausdorff
as well, and use the term quasi-compact to refer to a non-Hausdorff compact
space. The modern convention seems to be to use compact in the sense given
here, but the old definition is still occasionally encountered (particularly in the
French school).
∗ hCompacti created: h2013-03-21i by: hdjaoi version: h30503i Privacy setting: h1i
hDefinitioni h54D30i h81-00i h83-00i h82-00i h46L05i h22A22i
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You can reuse this document or portions thereof only if you do so under terms that are
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