Difference between revisions of "Hausdorff space"

Revision as of 18:50, 19 April 2015

Definition

Given a Topological space $(X,\mathcal{J})$ we say it is Hausdorff^[1] or satisfies the Hausdorff axiom if:

• For all $a,b\in X$ that are distinct there exists neighbourhoods to $a$ and $b$, $N_a$ and $N_b$ such that:
  • $N_a\cap N_b=\emptyset$

References

1. Jump up ↑ Introduction to topology - Mendelson - Third Edition