Monotone normality free of \(T_1\) axiom
The paper under review is a valuable contribution to the treatment of monotone normality without \(T_{1}\)-separation. The authors successfully avoid the closedness of singletons by considering their closures. With this idea, the authors characterize monotone normality without the \(T_{1}\)-axiom (Proposition 3.2) which up to now was known to hold under \(T_{1}\). Using their characterization, the authors are able to remove the \(T_{1}\)-axiom from the Tietze-type characterization of monotonically normal spaces due to \textit{I. Stares} [Commentat. Math. Univ. Carol. 36, No. 3, 563--578 (1995; Zbl 0882.54012)] and, besides, to prove it for functions with values in an appropriately based completely distributive lattice (Theorem 4.4).
scientific article; zbMATH DE number 5651931