continuous function

Definition (continuous map between topological spaces)

Define a continuous map between topological spaces $X$ and $Y$ as a mapping $f$ such that for every open set $V$ in $Y$, preimage $f^{-1}(V)$ is also an open set in $X$.

References

1. http://staff.ustc.edu.cn/~wangzuoq/Courses/18F-Manifolds/Notes/Lec01.pdf