Topology Proceedings 33 (2009), pp. 297-317

Coreflective subconstructs of the constructs of affine sets

Veerle Claes

For a topological construct, we give necessary and sufficient conditions to be isomorphic to a coreflective subconstruct of a category of affine sets. This means that the objects can be described isomorphically as sets structured by a collection of functions. We also characterize the hereditary coreflective subconstructs of the categories of affine sets and the subcategories constructed from an algebra stucture. We prove that these two types of subconstructs do not coincide. As an application of these results we find a relation between the affine sets over [0, ∞] and the metrically generated categories. Finally, we will give some examples of (T, V)-categories which can be embedded in the category of affine sets over V.

Keywords: affine set, hereditary coreflective subconstruct, initially dense object, metrically generated theory, (T, V)-category

Mathematics Subject Classification: 54A05, 54B30, 18B99

Document formats: PDF file 221.2 Kb

Topology Proceedings, Volume 33 (2009)
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