Subspace 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 space X is a subset S 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]

  1. ^ a b c tom Dieck, Tammo (2008), Algebraic topology, EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, p. 5, doi:10.4171/048, ISBN 978-3-03719-048-7, MR 2456045
  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, ISBN 9781118984574; see Section 26.2.4. Submanifolds, p. 59