Definition:Separation (Topology)

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

A separation $A \mid B$ of $T$ is a pair of open sets $A, B \in \tau$ such that:
 * $(1): \quad A$ and $B$ are non-empty
 * $(2): \quad A \cup B = S$
 * $(3): \quad A \cap B = \varnothing$

That is, such that $A$ and $B$ form a partition of the set $S$.

Also known as
A separation in this particular context is also known as a partition.

However, because the latter term has a definition in set theory, separation is preferred so as to reduce ambiguity and the possibility of confusion.

Also see

 * Definition:Connected Topological Space, one of whose properties is admitting no separation.


 * Components of Separation are Clopen