A Hausdorff HS-space which is not regular

Abstract

In this paper I disprove, with a counterexample, a theorem of H.J. Schmidt [6], which states that each Hausdorff HS-space is regular. M. Paoli and E. Ripoli [4] noted that the proof of this theorem is incorrect, but they left the statement open.

Keywords

• hausdorff and regular spaces
• closed sets