# continuous function

## 1. continuous function between topological spaces

- consider two topological spaces \((X, \cal{T})\) and \((X', \cal{T}')\). A function \(f: X\rightarrow X'\) is
*continuous*if for every open set \(V\in \cal{T}'\), the pre-image \(f^{-1}(V) = \{x \in X | f(x) \in V\}\) is an open set in \(\cal{T}\).