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LMCS
2006

Computably Based Locally Compact Spaces

13 years 3 months ago
Computably Based Locally Compact Spaces
tract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambda-calculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family of open subspaces and accompanying family of compact ones. This generalises Smyth's effectively given domains and Jung's Strong proximity lattices. Part of the data for a basis is the inclusion relation of compact subspaces within open ones, which is formulated in locale theory as the way-below relation on a continuous lattice. The finitary properties of this relation are characterised here, including the Wilker condition for the cover of a compact space by two open ones. The real line is used as a running example, being closely related to Scott's domain of intervals. ASD does not use th...
Paul Taylor 0002
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2006
Where LMCS
Authors Paul Taylor 0002
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