T1 space
= T1 space
{c}
{title2=$T_1$}
A <topological space> is T1 when every point is a <closed point>. Equivalently, for distinct $x,y$ there is an open set containing $x$ but not $y$, and an open set containing $y$ but not $x$. These open sets need not be disjoint. Every <Hausdorff space> is T1, but an infinite set with its <cofinite topology> is T1 without being Hausdorff.