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The Stacks project

Definition 5.6.3. Let f : X \to Y be a continuous map of topological spaces.

  1. We say f is a strict map of topological spaces if the induced topology and the quotient topology on f(X) agree (see discussion above).

  2. We say f is submersive1 if f is surjective and strict.

[1] This is very different from the notion of a submersion between differential manifolds! It is probably a good idea to use “strict and surjective” in stead of “submersive”.

Comments (1)

Comment #628 by Wei Xu on

A typo: "...topology on agree" should be "...topology on agree".

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