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Books > Science & Mathematics > Mathematics > Algebra
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Separation in Point-Free Topology (Paperback, 1st ed. 2021)
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Separation in Point-Free Topology (Paperback, 1st ed. 2021)
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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 inspiration for 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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