On functionally θ-normal spaces

[EN] 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.Kohli, J.; Das, A. (2005). On functionally θ-normal spaces. Applied General Topology. 6(1):1-14. doi:10.4995/agt.2005.1960.1146