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”.

Comment #628 by Wei Xu on

A typo: "...topology on $f(Y)$ agree" should be "...topology on $f(X)$ agree".

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