On functionally θ-normal spaces


  • J.K. Kohli University of Delhi
  • A.K. Das University Of Delhi




θ-closed (open) set, Regularly closed (open) set, Zero set, Regular Gδ-set, (weakly) (functionally) θ-normal space, (weakly) θ-regular space, Almost regular space, Mildly normal (≡ k-normal) space, Almost normal space, δ-normal space, δ-normally separated


Characterizations of functionally θ-normal spaces including the one that of Urysohn’s type lemma, are obtained. Interrelations among (functionally) θ-normal spaces and certain generalizations of normal spaces are discussed. It is shown that every almost regular (or mildly normal ≡ k-normal) θ-normal space is functionally θ-normal. Moreover, it is shown that every almost regular weakly θ-normal space is mildly normal. A factorization of functionally θ-normal space is given. A Tietze’s type theorem for weakly functionally θ-normal space is obtained. A variety of situations in mathematical literature wherein the spaces encountered are (functionally) θ-normal but not normal are illustrated.


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Author Biographies

J.K. Kohli, University of Delhi

Department of Mathematics

A.K. Das, University Of Delhi

Department of Mathematics


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How to Cite

J. Kohli and A. Das, “On functionally θ-normal spaces”, Appl. Gen. Topol., vol. 6, no. 1, pp. 1–14, Apr. 2005.