On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces

Abstract

We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that weak Hausdorffness is a sufficient condition for lenses and of quasi-lenses to form homeomorphic spaces, generalizing previously known results.

15 pages; removed Proposition 5.4, whose proof was wrong; added new Lemma 5.5 and Remark 5.6, solving a previously open question