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Apartness and Uniformity (Record no. 21886)

000 -LEADER
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003 - CONTROL NUMBER IDENTIFIER
control field OSt
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20140310151123.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 110907s2011 gw | s |||| 0|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783642224157
978-3-642-22415-7
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number QA75.5-76.95
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 004.0151
Edition number 23
264 #1 -
-- Berlin, Heidelberg :
-- Springer Berlin Heidelberg,
-- 2011.
912 ## -
-- ZDB-2-SCS
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Bridges, Douglas S.
Relator term author.
245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE
Title Apartness and Uniformity
Medium [electronic resource] :
Remainder of title A Constructive Development /
Statement of responsibility, etc by Douglas S. Bridges, Luminiţa Simona Vîţă.
300 ## - PHYSICAL DESCRIPTION
Extent XIV, 198 p.
Other physical details online resource.
440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE
Title Theory and Applications of Computability, In cooperation with the association Computability in Europe,
International Standard Serial Number 2190-619X
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note The Constructive Framework -- Point-Set Apartness -- Apartness Between Sets -- Postlude: Paths to Topology -- References -- Index.
520 ## - SUMMARY, ETC.
Summary, etc The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-based theory of proximity spaces provides some guidance for the theory of apartness, the notion of nearness/proximity does not embody enough algorithmic information for a deep constructive development. The use of constructive (intuitionistic) logic in this book requires much more technical ingenuity than one finds in classical proximity theory -- algorithmic information does not come cheaply -- but it often reveals distinctions that are rendered invisible by classical logic. In the first chapter the authors outline informal constructive logic and set theory, and, briefly, the basic notions and notations for metric and topological spaces. In the second they introduce axioms for a point-set apartness and then explore some of the consequences of those axioms. In particular, they examine a natural topology associated with an apartness space, and relations between various types of continuity of mappings. In the third chapter the authors extend the notion of point-set (pre-)apartness axiomatically to one of (pre-)apartness between subsets of an inhabited set. They then provide axioms for a quasiuniform space, perhaps the most important type of set-set apartness space. Quasiuniform spaces play a major role in the remainder of the chapter, which covers such topics as the connection between uniform and strong continuity (arguably the most technically difficult part of the book), apartness and convergence in function spaces, types of completeness, and neat compactness. Each chapter has a Notes section, in which are found comments on the definitions, results, and proofs, as well as occasional pointers to future work. The book ends with a Postlude that refers to other constructive approaches to topology, with emphasis on the relation between apartness spaces and formal topology. Largely an exposition of the authors' own research, this is the first book dealing with the apartness approach to constructive topology, and is a valuable addition to the literature on constructive mathematics and on topology in computer science. It is aimed at graduate students and advanced researchers in theoretical computer science, mathematics, and logic who are interested in constructive/algorithmic aspects of topology.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Computer science.
Topical term or geographic name as entry element Information theory.
Topical term or geographic name as entry element Global analysis (Mathematics).
Topical term or geographic name as entry element Logic, Symbolic and mathematical.
Topical term or geographic name as entry element Topology.
Topical term or geographic name as entry element Computer Science.
Topical term or geographic name as entry element Theory of Computation.
Topical term or geographic name as entry element Mathematics of Computing.
Topical term or geographic name as entry element Topology.
Topical term or geographic name as entry element Analysis.
Topical term or geographic name as entry element Mathematical Logic and Foundations.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Vîţă, Luminiţa Simona.
Relator term author.
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text Printed edition:
International Standard Book Number 9783642224140
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier http://dx.doi.org/10.1007/978-3-642-22415-7
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type E-Book
Copies
Price effective from Permanent location Date last seen Not for loan Date acquired Source of classification or shelving scheme Koha item type Damaged status Lost status Withdrawn status Current location Full call number
2014-04-23AUM Main Library2014-04-23 2014-04-23 E-Book   AUM Main Library004.0151