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Frames and Locales Topology Without Points 1st Edition by Jorge Picado, Ales Pultr ISBN 303480153X 9783034801539

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Frames and Locales Topology Without Points 1st Edition Jorge Picado Digital Instant Download

Author(s): Jorge Picado, Aleš Pultr (auth.)
ISBN(s): 9783034801539, 303480153X
Edition: 1
File Details: PDF, 6.02 MB
Year: 2012
Language: english
SKU: EB-2407652 Category: Tags: ,

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ISBN 10: 303480153X 
ISBN 13: 9783034801539
Author: Jorge Picado, Ales Pultr

Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. 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. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results previously dependent on choice principles became constructive. The result is often a smoother, rather than a more entangled, theory. No monograph of this nature has appeared since Johnstone’s celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present.  Most of the material appears here in book form for the first time or is presented from new points of view. Two appendices provide an introduction to some requisite concepts from order and category theories.

Frames and Locales Topology Without Points 1st Table of contents:

Chapter I Spaces and Lattices of Open Sets
Chapter II Frames and Locales. Spectra
Chapter III Sublocales
Chapter IV Structure of Localic Morphisms.The Categories Loc and Frm
Chapter V Separation Axioms
Chapter VI More on Sublocales
Chapter VII Compactness and Local Compactness
Chapter VIII (Symmetric) Uniformity and Nearness
Chapter IX Paracompactness
Chapter X More about Completion
Chapter XI Metric Frames
Chapter XII Entourages. Asymmetric Uniformity
Chapter XIII Connectedness
Chapter XIV The Frame of Reals and Real Functions
Chapter XV Localic Groups

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Tags: Jorge Picado, Ales Pultr, Locales Topology