Abstract
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) e 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 τAfor 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).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
