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


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).


Topological Space Explicit Description Coarse Topology Reflective Subcategory Epireflective Subcategory 


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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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