TITLE: Cantor Set (Hausdorff)
QUESTION [9 upvotes]: Is the Cantor set Hausdorff? Which separability axioms it has?
I know that $\mathbb R$ are Hausdorrf is it enough?
Like the Cantor set is compact if it was Hausdorff then the Cantor set would be normal and regular, and it would be T1 for inherited? Or it has another axioms?
Thanks for your help

REPLY [5 votes]: "I know that R (real numbers) are Hausdor[f]f is it enough?"
Yes, it is. Suppose $X$ is a Hausdorff space and $Y\subseteq X$ has the subspace topology.
Given two points $x,y\in Y,$ there are open sets $U,V\subseteq X$ with $x\in U,$ $y\in V,$ and $U\cap V=\varnothing.$ The intersections of $U$ and $V$ with $Y$ are open subsets of $Y$ and contain $x$ and $y$ as members and do not intersect each other.