Overview

This book is the first systematic treatment of this area so far scattered in a vast number of articles. As in classical topology, concrete problems require restricting the (generalized point-free) spaces by various conditions playing the roles of classical separation axioms. These are typically formulated in the language of points; but in the point-free context one has either suitable translations, parallels, or satisfactory replacements. The interrelations of separation type conditions, their merits, advantages and disadvantages, and consequences are discussed. Highlights of the book include a treatment of the merits and consequences of subfitness, various approaches to the Hausdorff's axiom, and normality type axioms. Global treatment of the separation conditions put them in a new perspective, and, a.o., gave some of them unexpected importance. The text contains a lot of quite recent results; the reader will see the directions the area is taking, and may find inspirationfor her/his further work. The book will be of use for researchers already active in the area, but also for those interested in this growing field (sometimes even penetrating into some parts of theoretical computer science), for graduate and PhD students, and others. For the reader's convenience, the text is supplemented with an Appendix containing necessary background on posets, frames and locales.

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9783030534813

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The book is very well-written with great attention to detail, making it a pleasure to read and, on top of covering a vast body of material ... . the monograph under review ... can only be highly recommended: they constitute a comprehensive source of information and insights regarding pointfree topology, which will be of great interest and value to researchers already working in the field, to mathematicians who want to study pointfree topology and to general topologists ... . (Mark Sioen, zbMATH 1486.54001, 2022)

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