Definition:Separated

Sets
Let $\left({X, \vartheta}\right)$ be a topological space.

Let $A, B \subseteq X$ such that:
 * $A^- \cap B = A \cap B^- = \varnothing$

where $A^-$ denotes the closure of $A$ in $X$.

Then $A$ and $B$ are described as separated.

Points
Let $\left({X, \vartheta}\right)$ be a topological space.

Let $x, y \in X$ such that both of the following hold:


 * $\exists U \in \vartheta: x \in U, y \notin U$
 * $\exists V \in \vartheta: y \in V, x \notin V$

Then $x$ and $y$ are described as separated.