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Frames and Locales

Topology without points
BuchKartoniert, Paperback
398 Seiten
Englisch
Springererschienen am22.10.2011
The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects.mehr
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BuchKartoniert, Paperback
EUR32,09
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Produkt

KlappentextThe concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects.
ZusammenfassungWith a wealth of unpublished material and useful appendices on the background, this is the first monograph on the topic for more than two decades and is intended to bridge the time span between Johnstone's 1983 paper Stone Spaces and current theory.
Details
ISBN/GTIN978-3-0348-0153-9
ProduktartBuch
EinbandartKartoniert, Paperback
Verlag
Erscheinungsjahr2011
Erscheinungsdatum22.10.2011
ReiheFrontiers in Mathematics
Seiten398 Seiten
SpracheEnglisch
Gewicht695 g
IllustrationenXIX, 398 p.
Artikel-Nr.10364352

Inhalt/Kritik

Inhaltsverzeichnis
Preface.- Introduction.- I. Spaces and lattices of open sets.- II. Frames and locales. Spectra.- III. Sublocales.- IV. Structure of localic morphisms. The categories Loc and Frm.- V. Separation axioms.- VI. More on sublocales.-VII. Compactness and local compactness.- VIII. (Symmetric) uniformity and nearness.- IX. Paracompactness.- X. More about completion.- XI. Metric frames.- XII. Entourages, non-symmetric uniformity.- XIII. Connectedness.- XIV. The frame of reals and real functions.- XV. Localic groups.- Appendix I: Posets.- Appendix II: Categories.- Bibliography.- Index of Notation.- Index.mehr
Kritik
From the reviews:

"The book covers, in a comprehensive and self-contained way, the development of point-free topology in the last 30 years ... . The book ends with two short appendices containing those facts about partially ordered sets and categories needed in the book. In conclusion, this is a very good book; it is nicely written and is highly recommended for anyone wishing to gain an overview of point-free topology." (Javier Gutiérrez García, Mathematical Reviews, Issue 2012 j)

"The book starts with a recount of sobriety and the TD-axiom, which is then quickly followed by the definition of the category of locales, various facets of spectra, the usual adjunctions and several criteria for spatiality. ... this book is an erudite account of the current status of pointfree topology, written beautifully in the authors' inimitable style. It is both easily accessible to a complete beginner, and an excellent source of reference for the mature pointfree practitioner." (Themba Dube, Zentralblatt MATH, Vol. 1231, 2012)

"In a total of fifteen chapters the reader is taken from spaces and lattices of open sets, through a thorough discussion of the notions of frames and locales ... . book ends (modulo its appendices) with a discussion of localic groups ... together with frames, that's what this entire book is ultimately all about. ... is quite-well written: it's a clear and thorough treatment of what is really rather an important subject, which is to say, a greatly underappreciated one." (Michael Berg, The Mathematical Association of America, April, 2012)mehr