A subspace of a Hausdorff space is Hausdorff.

Let X be Hausdorff and

Since Y is a subspace, where C is some open set in X.

Let

is the intersection of open sets so it is open. Therefore, where U and V are open sets in . Again since is open, U and V can be constructed in such a manner that .

Thus, the subspace is Hausdorff.

Correct?