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Open subset of open subspace is open

From Topospaces

Revision as of 00:54, 25 January 2012 by Vipul (talk | contribs) (Created page with "==Statement== Suppose <math>X</math> is a topological space and <math>V</math> is an open subset of <math>X</math>. Suppose <math>U</math> is a subset of <math>V</mat...")

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Statement

Suppose $X$ is a topological space and $V$ is an open subset of $X$ . Suppose $U$ is a subset of $V$ that is an open subset of $V$ under the subspace topology on $V$ . Then, $U$ is also an open subset of $X$ .

Related facts

Closed subset of closed subspace is closed

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