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Subspace topology
Inherited topology
"Induced topology" redirects here. For the topology generated by a family of functions, see Initial topology.
In topology and related areas of mathematics, a subspace of a topological spaceX is a subsetS of X which is equipped with a topology induced from that of X called the subspace topology[1] (or the relative topology,[1] or the induced topology,[1] or the trace topology).[2]
^Pinoli, Jean-Charles (June 2014), "The Geometric and Topological Framework", Mathematical Foundations of Image Processing and Analysis 2, Wiley, pp. 57–69, doi:10.1002/9781118984574.ch26, ISBN9781118984574; see Section 26.2.4. Submanifolds, p. 59