On Weakly Hausdorff Spaces and Locally Strongly Sober Spaces
Keywords:
lens, locally strongly sober, Stone duality, temperate frame, weakly HausdorffAbstract
We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Klaus Keimel and Jimmie D. Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that weak Hausdorffness is a suffcient condition for lenses and of quasi-lenses to form homeomorphic spaces, generalizing previously known results.
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