Is the quotient map between topological spaces always continuous? If this is not the case, what conditions need to be satisfied for this to be true? Thanks for the help!
2026-04-03 03:31:17.1775187077
Quotient space between topological spaces
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Yes, a quotient map is by definition continuous. Specifically, a map $f:X\to Y$ is a quotient map if it is continuous, surjective, and the topology on $Y$ is the finest topology for which $f$ is continuous.