Relative Topology

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X.

For example, in the relative topology of the interval S=[0,1] induced by the Euclidean topology of the real line, the half-open interval [0,1/2) is open since it coincides with [0,1] intersection (-1,1/2). This example shows that an open set of the relative topology of S need not be open in the topology of X.

This entry contributed by Margherita Barile

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

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