Exact Filters and Joins of Closed Sublocales

Exact Filters and Joins of Closed Sublocales

We prove, for a general frame, that the sublocales that can be represented as joins of closed ones are, somewhat surprisingly, in a natural one-to-one correspondence with the filters closed under exact meets, and explain some subfit facts from this perspective. Furthermore we discuss the filters ass...

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Veröffentlicht in:Applied categorical structures 2020-08, Vol.28 (4), p.655-667
Hauptverfasser: Ball, R. N., Moshier, M. A., Pultr, A.
Format: Artikel
Sprache:eng
Schlagworte:
Convex and Discrete Geometry
Geometry
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Theory of Computation
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Zusammenfassung:We prove, for a general frame, that the sublocales that can be represented as joins of closed ones are, somewhat surprisingly, in a natural one-to-one correspondence with the filters closed under exact meets, and explain some subfit facts from this perspective. Furthermore we discuss the filters associated in a similar vein with the fitted sublocales.
ISSN:0927-2852
1572-9095
DOI:10.1007/s10485-020-09593-y