Epiregular topological spaces



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

54D15 54B10 


  1. 1.
    Alexandroff, P.S., Urysohn, P.S.: Mémoire sur les espaces topologiques compacts, vol. 14. Verh. Akad. Wetensch, Amsterdam (1929)MATHGoogle Scholar
  2. 2.
    AlZahrani, S., Kalantan, L.: Epinormality. J. Nonlinear Sci. Appl. 9, 5398–5402 (2016)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Engelking, R.: General Topology. PWN, Warszawa (1977)MATHGoogle Scholar
  4. 4.
    Engelking, R.: On the Double Circumference of Alexandroff. Bull. Acad. Pol. Sci. Ser. Astron. Math. Phys. 16(8), 629–634 (1968)MathSciNetMATHGoogle Scholar
  5. 5.
    Gruenhage, G.: Generalized metric spaces. In: Handbook of Set Theoretic Topology, pp. 428–434. North Holland, Amsterdam (1984)Google Scholar
  6. 6.
    Kalantan, L., Allahabi, F.: On almost normal. Demonstr. Math. xli(4), 961–968 (2008)MATHGoogle Scholar
  7. 7.
    Mrsevic, M., Reilly, I.L., Vamanamurthy, M.K.: On semi-regularization topologies. J. Austral. Math. Soc. (Ser.) 38, 40–54 (1985)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Patty, C.W.: Foundations of topology. Jones and Bartlett, Sudbury (2008)MATHGoogle Scholar
  9. 9.
    Steen, L., Seebach, J.A.: Counterexamples in Topology. Dover Publications, INC., New York (1995)MATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTaif UniversityTaifSaudi Arabia

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