Definition:Hausdorff Space

Let $$X$$ be a topological space with topology $$\vartheta$$ where $$x,y \in X$$.

If $$\exists U, V \in \vartheta$$ such that $$x \in U$$ and $$y \in V$$ where $$U \cap V = \varnothing$$, then $$X$$ is a Hausdorff space or $$T_2$$ space.

For more on the notation $$T_2$$, see the page on separation axioms.