On functionally θ-normal spaces

J.K. Kohli, A.K. Das


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.


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

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1. A class of spaces containing all generalized absolutely closed (almost compact) spaces
J.K. Kohli, A.K. Das
Applied General Topology  vol: 7  issue: 2  first page: 233  year: 2006  
doi: 10.4995/agt.2006.1926

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt