2014/07/04 by Endre Makai, E. Makai Jr, Makai, E. +1
Mathematics · #18C05 #18C10 #54E15 (Primary) #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #Secondary (54B30) #math.CT #math.GN #msc:18C05 #msc:18C10 #msc:54E15
paper · pdf · doi:10.48550/arxiv.1407.1210
20 pages
arxiv created 2014/07/04 · openalex publication_date 2014/07/04 · arxiv updated 2014/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The epireflective subcategories of \boldTop, that are closed under epimorphic (or bimorphic) images, are \X | |X| ≤ 1 \ , \X | X is indiscrete\ and \boldTop. The epireflective subcategories of \boldT2Unif, closed under epimorphic images, are: \X | |X| ≤ 1 \ , \X | X is compact T2 \ , \X | covering character of X is ≤ λ0 \ (where λ0 is an infinite cardinal), and \boldT2Unif. The epireflective subcategories of \boldUnif, closed under epimorphic (or bimorphic) images, are: \X | |X| ≤ 1 \ , \X | X is indiscrete\ , \X | covering character of X is ≤ λ0 \ (where λ0 is an infinite cardinal), and \boldUnif. The epireflective subcategories of \boldTop, that are algebraic categories, are \X | |X| ≤ 1 \ , and \X | X is indiscrete\ . The subcategories of \boldUnif, closed under products and closed subspaces and being varietal, are \X | |X| ≤ 1 \ , \X | X is indiscrete\ , \X | X is compact T2 \ . The subcategories of \boldUnif, closed under products and closed subspaces and being algebraic, are \X | X is indiscrete \ , and all epireflective subcategories of \X | X is compact T2 \ . Also we give a sharpened form of a theorem of Kannan-Soundararajan about classes of T3 spaces, closed for products, closed subspaces and surjective images.