Definition · applies to functions

Undergraduate

A function $f : \reals^n \to \reals^m$ is called open if the image of every open set $U$ in $\reals^n$ is an open set $f(U)$ in $\reals^m$.

Graduate

Consider topological spaces $S$ and $T$. A function $f : S\to T$ is called open if the image of every open set $U$ in $S$ is an open set $f(U)$ in $T$.

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