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Annali di Matematica Pura ed Applicata

, Volume 145, Issue 1, pp 337–346 | Cite as

A diagonal theorem for epireflective subcategories of top and cowellpoweredness

  • E. Giuli
  • M. Hušek
Article

Summary

For a quotient-reflective subcategoryAof the category Topof topological spaces the following «diagonal theorem» is proved: a topological space (X,τ)belongs toAiff the diagonal Δxis (τ×τ) A -closed, where, for (X, ρ) ε Top, σAdenotes the coarsest topology on X which has as closed subsets all the equalizers of pairs of continuous maps with codomain inA.Furthermore an explicit description of τ A for several quotient reflective subcategories defined by means of properties of subspaces is given. It is shown that one of them is not co-(well-powered).

Keywords

Topological Space Explicit Description Coarse Topology Reflective Subcategory Epireflective Subcategory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1985

Authors and Affiliations

  • E. Giuli
    • 1
  • M. Hušek
    • 2
  1. 1.Department of Pure and Applied MathematicsUniversityL'AquilaItaly
  2. 2.Matematický UstavKarlovy UniversityPraha 8Czechoslovakia

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