# Definition A [[map]] $f:X \rightarrow Y$ is *continuous* if the [[Domain, Co-domain, Image|inverse image]] of an [[open set]] in $Y$ is an open set in $X$. The opposite definition doesn't work (in terms of the image), even though it's used in some books. Here, $X$ and $Y$ are [[Topological Space|topological spaces]], otherwise, we cannot define open sets and thus cannot define continuity. More generally, $f$ is continuous on $X$ (or more simply, *continuous*) if it is continuous for all points $x \in X$.