Monotone normality free of \(T_1\) axiom
type: Item
instance of: scholarly article
title: Monotone normality free of \(T_1\) axiom
zbMATH Open document ID: 1240.54077
author: Javier Gutiérrez García
author: Iraide Mardones-Pérez
author: María Angeles de Prada Vicente
published in: Acta Mathematica Hungarica
publication date: 2009-12-29T00:00:00Z
review text: 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).
reviewed by: Tomasz Kubiak
Mathematics Subject Classification ID: 54D15
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54C99
Mathematics Subject Classification ID: 06D10
zbMATH DE Number: 5651931
zbMATH Keywords: monotone normality
zbMATH Keywords: completely distributive lattice
zbMATH Keywords: Raney relation
zbMATH Keywords: \(\triangleleft\)-separable
zbMATH Keywords: lower semicontinuous function
zbMATH Keywords: upper semicontinuous function
zbMATH Keywords: extension theorem
MaRDI profile type: Publication
DOI: 10.1007/S10474-009-7234-3
description: scientific article; zbMATH DE number 5651931