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＜電子ブック＞
Separation in Point-Free Topology / by Jorge Picado, Aleš Pultr

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Birkhäuser)
出版年	2021
大きさ	XXI, 281 p. 40 illus., 1 illus. in color : online resource
著者標目	*Picado, Jorge author Pultr, Aleš author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Algebra, Homological LCSH:Topology FREE:Order, Lattices, Ordered Algebraic Structures FREE:Category Theory, Homological Algebra FREE:Topology
一般注記	Introduction -- Separation in spaces -- Subfitness, and basics of fitness -- Subfitness, and basics of fitness -- Summarizing low separation -- Regularity and fitness -- Complete regularity -- Complete regularity -- Normality -- Complete regularity -- Scatteredness. Joins of closed sublocales -- Subfit, fit, open and complete -- Appendix 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 HTTP:URL=https://doi.org/10.1007/978-3-030-53479-0

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