在数学的拓扑学中，开映射是两个拓扑空间之间的映射，使得任何开集的像都是开集；闭映射是两个拓扑空间之间的映射，使得任何闭集的像都是闭集。所以f: X → Y是开映射（闭映射），如果X中的开集（闭集）在f下的像都为Y的开集（闭集）。

开映射和闭映射的定义中，并不要求映射连续。与之比较，映射f: X → Y为连续映射的定义，是所有Y的开集的原像为X的开集，也可等价地定义为所有Y的闭集的原像为X的闭集。虽然开映射和闭映射的定义，似较连续映射为自然，但在拓扑学中其重要性不及连续映射。

In topology, an open map is a function between two topological spaces which maps open sets to open sets. That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function which maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa.