A non-Hausdorff space with a Hausdorff subspace

941 Views Asked by Bumbble Comm At 26 Mar 2026 - 12:41

Can anyone give an example of a non-Hausdorff space that contains a Hausdorff subspace?

There are 2 best solutions below

Bumbble Comm On 10 Mar 2017 - 8:22

A point is Hausdorff, so any non-Hausdorff space gives examples.

Bumbble Comm On 10 Mar 2017 - 8:24

It is enough to consider the line with two origins, and than consider one of this lines as a subspace.