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Categories of closure spaces and corresponding lattices. (English) Zbl 0813.18003

The well-known characterization of the closed-set lattices of topological spaces, as the duals of complete Heyting algebras with enough primes, is here extended to closed-set lattices of closure spaces, by deleting the distributivity requirement in an appropriate way. The category of closure spaces satisfying (the closure-space analogue of) Aull and Thron’s axiom \(T_ D\) is shown to be equivalent to an appropriate category of lattices, and a number of (straightforward) applications are given.

MSC:

18B30 Categories of topological spaces and continuous mappings (MSC2010)
54A05 Topological spaces and generalizations (closure spaces, etc.)
06B23 Complete lattices, completions
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References:

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