Open Cover

A collection of open sets of a topological space whose union contains a given subset. For example, an open cover of the real line, with respect to the Euclidean topology, is the set of all open intervals (-n,n), where n in N.

The set of all intervals (1/n,1), where n in N\{0}, is an open cover of the open interval (0,1).

See also

Compact Space, Cover

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Open Cover." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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