Titlebook: Separation in Point-Free Topology; Jorge Picado,Aleš Pultr Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive lice

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Subfitness and Basics of Fitness,126, 1938) published in 1938 (already briefly mentioned in the Introduction), Wallman presented a compactification technically based on lattice theoretic principles, and proved that to determine the homology type of a space . one needs only the lattice of closed sets. When doing that, he needed a la

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Regularity and Fitness,terest in conditions that would capture classical separation phenomena as convincingly as possible in the new, more general, context. Classical separation axioms are typically formulated in the language of points and point-dependent notions; hence, one looked for equivalent formulations, or imitated

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Normality,t there is not much interest about it in the extended context. On the contrary, besides the new view one gains of the plain normality itself and of its relations to the other axioms one has natural strengthenings (and, in a smaller extent also weakenings) that are not so obviously point-free and the

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More on Normality and Related Properties, 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 .. Then, in the penultimate section we prove and discuss the Katětov–Tong insertion theorem,

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