A topological space (X, \(\tau \)) is called epiregular if there is a coarser topology \(\tau \)\(^\prime \) on X such that (X, \(\tau \)\(^\prime )\) is \(T_3\). We investigate this property and present some examples to illustrate the relationships between epiregular, epinormal, submetrizable, semiregular and almost regular.
Regular Epiregular Epinormal Semiregular Submetrizable Almost regular Regularly open Regularly closed
Mathematics Subject Classification
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Alexandroff, P.S., Urysohn, P.S.: Mémoire sur les espaces topologiques compacts, vol. 14. Verh. Akad. Wetensch, Amsterdam (1929)MATHGoogle Scholar