$\textbf{$T_3$ space / regular Hausdorff space}$
A $T_2$ space $X$ is called a $T_3$ space or regular Hausdorff space if for any point $x$ and closed set $F$ not containing $x$ there are disjoint open sets $U$ and $V$ with $x\in U$ and $F\subset V$.
Note: The condition $T_2$ can be equivalently changed to $T_1$.
$\textbf{$T_3$ space / regular Hausdorff space}$
A $T_2$ space $X$ is called a $T_3$ space or regular Hausdorff space if for any point $x$ and closed set $F$ not containing $x$ there are disjoint open sets $U$ and $V$ with $x\in U$ and $F\subset V$.
Note: The condition $T_2$ can be equivalently changed to $T_1$.
copied
๐โย ๐ฌ๐ฉ๐๐๐ย /ย ๐ซ๐๐ ๐ฎ๐ฅ๐๐ซย ๐๐๐ฎ๐ฌ๐๐จ๐ซ๐๐ย ๐ฌ๐ฉ๐๐๐
A ๐โ space ๐ is called a ๐โ space or regular Hausdorff space if for any point ๐ฅ and closed set ๐น not containing ๐ฅ there are disjoint open sets ๐ and ๐ with ๐ฅโ๐ and ๐นโ๐.
Note: The condition ๐โ can be equivalently changed to ๐โ.