On classes of T0 spaces admitting completions | Zendy

Eraldo Giuli | Zendy

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On classes of T0 spaces admitting completions

Author(s) -

Eraldo Giuli

Publication year - 2003

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2003.2016

Subject(s) - mathematics , class (philosophy) , metric space , tychonoff space , expansive , subcategory , new class , property (philosophy) , topological space , pure mathematics , discrete mathematics , combinatorics , computer science , philosophy , compressive strength , materials science , epistemology , artificial intelligence , economics , market economy , composite material

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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