On classes of T0 spaces admitting completions


  • Eraldo Giuli Università di L'Aquila




Affine set, T0, Sober and injective space, Compact space, Completion, Zariski closure, topological category, Coreflective subcategory


For a given class X of T0 spaces the existence of a subclass C, having the same properties that the class of complete metric spaces has in the class of all metric spaces and non-expansive maps, is investigated. A positive example is the class of all T0 spaces, with C the class of sober T0 spaces, and a negative example is the class of Tychonoff spaces. We prove that X has the previous property (i.e., admits completions) whenever it is the class of T0 spaces of an hereditary coreflective subcategory of a suitable supercategory of the category Top of topological spaces. Two classes of examples are provided.


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Author Biography

Eraldo Giuli, Università di L'Aquila

Department of Mathematics


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How to Cite

E. Giuli, “On classes of T0 spaces admitting completions”, Appl. Gen. Topol., vol. 4, no. 1, pp. 143–155, Apr. 2003.



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