Meets of spatial sublocales
Tao Lu, Wei He, and Xijuan Wang
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 17, Number 2
(2010), 243-250.
Abstract
It is well known that the functor $\Omega: {\bf Sp} \rightarrow {\bf Loc}$ does not preserve meets of subspaces. More generally, the meet of a family of spatial sublocales of a locale is in general not spatial. In this paper, we will give a characterization for those topological spaces for which the functor $\Omega$ preserves meets of subspaces. As a corollary, we give some characterizations for the meet of some spatial sublocales of a locale to be spatial.
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Bulletin of the Belgian Mathematical Society - Simon Stevin
