For example, in the relative topology of the interval induced by the Euclidean topology of the real line, the half-open interval is open since it coincides with . This example shows that an open set of the relative topology of need not be open in the topology of .
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. https://mathworld.wolfram.com/RelativeTopology.html