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Categories of diametric frames. (English) Zbl 0683.54008
This paper is concerned with extending metric structure to pointless spaces (frames or locales). The distance function is replaced by a “diameter” function from the frame to the non-negative reals satisfying certain natural properties (monotonicity, subadditivity). Two additional properties are postulated to obtain a well-behaved theory; the resulting structures are called diametric frames. Various categories of diametric frames are considered, and the adjoint relationship between the open-set functor and the spectrum functor established. The paper closes with a consideration of limits and colimits in this setting.
Reviewer: J.D.Lawson

MSC:
54A05 Topological spaces and generalizations (closure spaces, etc.)
18B30 Categories of topological spaces and continuous mappings (MSC2010)
54H12 Topological lattices, etc. (topological aspects)
06B30 Topological lattices
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References:
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