Monotone normality and stratifiability from a pointfree point of view

Monotone normality is usually defined in the class of T1 spaces. In this paper we study it under the weaker condition of subfitness, a separation condition that originates in pointfree topology. In particular, we extend some well known characterizations of these spaces to the subfit context (notably...

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Bibliographic Details
Published in:Topology and its applications 2014-05, Vol.168, p.46-65
Main Authors: Gutiérrez García, Javier, Picado, Jorge, de Prada Vicente, María Ángeles
Format: Article
Language:English
Subjects:
Borges operator
Closed map
Frame
Hereditary monotone normality
Locale
Monotone normality
Monotonically normal operator
Open sublocale
Stratifiability
Subfit frame
Subfit space
Weakly subfit frame
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Summary:Monotone normality is usually defined in the class of T1 spaces. In this paper we study it under the weaker condition of subfitness, a separation condition that originates in pointfree topology. In particular, we extend some well known characterizations of these spaces to the subfit context (notably, their hereditary property and the preservation under surjective continuous closed maps) and present a similar study for stratifiable spaces, an important subclass of monotonically normal spaces. In the second part of the paper, we extend further these ideas to the lattice theoretic setting. In particular, we give the pointfree analogues of the previous results on monotonically normal spaces and introduce and investigate the natural pointfree counterpart of stratifiable spaces.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2014.02.020