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 ≡ κ-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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Sergey Fomin (1943) studied this question.
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