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Separation in point-free topology

Picado, Jorge.

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Separation in point-free topology

Record Type:	Electronic resources : Monograph/item
Title/Author:	Separation in point-free topology/ by Jorge Picado, Ales Pultr.
Author:	Picado, Jorge.
other author:	Pultr, Ales.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xxi, 281 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Topology. -
Online resource:	https://doi.org/10.1007/978-3-030-53479-0
ISBN:	9783030534790

Separation in point-free topology
Picado, Jorge.

Separation in point-free topology[electronic resource] /by Jorge Picado, Ales Pultr. - Cham :Springer International Publishing :2021. - xxi, 281 p. :ill., digital ;24 cm.

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.

ISBN: 9783030534790

Standard No.: 10.1007/978-3-030-53479-0doiSubjects--Topical Terms:

522026
Topology.

LC Class. No.: QA611 / .P533 2021

Dewey Class. No.: 514

Separation in point-free topology
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505 0 $a 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.
520 $a 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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