在拓扑学和相关数学领域中，离散空间是特别简单的一种拓扑空间，在其中点都在特定意义下是相互孤立的。

给定集合X:

对于任何。在这种情况下被称为离散度量空间或孤点空间。

度量空间被称为“一致离散”的，如果存在使得对于任何，要幺要幺。在度量空间底层的拓扑空间可以是离散的，而没有一致离散的度量：例如在实数的集合{1, 1/2, 1/4, 1/8, ...}上的平常度量。

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set, i.e., it defines all subsets as open sets. In particular, each singleton is an open set in the discrete topology.