Overview
A Hausdorff space is a topological space where distinct points in the space have distinct neighborhoods. That is, for points {% x %} and {% y %} such that {% x \neq y %}, there exist neighborhoods {% U_1 %}, {% U_2 %} such that
{% U_1 \cap U_2 = \varnothing %}
and {% x \in U_1 %} and {% y \in U_2 %}.