More on Normality and Related Properties

Jorge Picado and Aleš Pultr
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Jorge Picado: University of Coimbra, CMUC, Department of Mathematics
Aleš Pultr: Charles University, Department of Applied Mathematics

Chapter Chapter VIII in Separation in Point-Free Topology, 2021, pp 155-185 from Springer

Abstract: Abstract Here we start with two more variants of normality. There is the perfect normality, which turns out to be a conjunction of the classical perfectness (which is slightly different in the point-free context due to the different behaviour of sublocales and subspaces) and normality; in a way it can be viewed as a weaker form of metrizability. Next we deal with the technically important collectionwise normality. Then, in the penultimate section we prove and discuss the Katětov–Tong insertion theorem, using (to advantage) the techniques of the point-free real line. We finish with a certain duality between normality and extremal disconnectedness that allows to translate several results concerning normality to facts about extremal disconnected frames.

Date: 2021
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DOI: 10.1007/978-3-030-53479-0_8

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