A continuous map $q:(X,T)\to (X’,T’)$ is said to be a quotient map if

1. $q$ is surjective
2. defining the equivalence relation in $X$ given by $x\sim y \Longleftrightarrow q(x)=q(y)$, the induced map $\bar q: (\bar X,\bar T) \to (X’,T’)$ (which is bijective and continuous) is a homeomorphism