UID:
almafu_9960119114702883
Umfang:
1 online resource (xiii, 300 pages) :
,
digital, PDF file(s).
Ausgabe:
1st ed.
ISBN:
0-511-89733-2
Serie:
Cambridge tracts in mathematics ; 79
Inhalt:
A chain condition is a property, typically involving considerations of cardinality, of the family of open subsets of a topological space. (Sample questions: (a) How large a fmily of pairwise disjoint open sets does the space admit? (b) From an uncountable family of open sets, can one always extract an uncountable subfamily with the finite intersection property. This monograph, which is partly fresh research and partly expository (in the sense that the authors co-ordinate and unify disparate results obtained in several different countries over a period of several decades) is devoted to the systematic use of infinitary combinatorial methods in topology to obtain results concerning chain conditions. The combinatorial tools developed by P. Erdös and the Hungarian school, by Erdös and Rado in the 1960s and by the Soviet mathematician Shanin in the 1940s, are adequate to handle many natural questions concerning chain conditions in product spaces.
Anmerkung:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Frontmatter -- Contents -- Introduction -- ERRATA -- Acknowledgements -- Some infinitary combinatorics -- Notes for Chapter 1 -- Introducing the chain conditions -- Chain conditions -- The λ-Souslin numbers -- Reduction to compact Hausdorff spaces -- Notes for Chapter 2 -- Chain conditions in products -- Product theorems for regular cardinals -- Product theorems for singular cardinals -- Chain conditions in powers -- The numbers Sλ ((XI )K) -- Notes for Chapter 3 -- Classes of calibres, using Σ-products -- Notes for Chapter 4 -- Calibres of compact spaces -- Strongly S(X)-inaccessible cardinals as calibres -- (Pre-) calibres for Pλ+ -spaces and λ+ -box product s -- Calibres of compact spaces: the 'exceptional' case -- Examples on calibres -- Notes for Chapter 5 -- Strictly positive measures -- Characterization of spaces with a strictly positive measure -- Spaces with a strictly positive measure -- The properties Kα,n -- Gaifman's example -- The example of Argyros -- The Galvin-Hajnal example -- Property (**) for non-compact spaces -- Notes for Chapter 6 -- Between property (K) and the countable chain condition -- Kunen's example -- The Laver-Galvin example -- Notes for Chapter 7 -- Classes of compact-calibres, using spaces of ultrafilters -- Notes for Chapter 8 -- Pseudo-compactness numbers: examples -- Notes for Chapter 9 -- Continuous functions on product spaces -- Notes for Chapter 10 -- Appendix: preliminaries -- A Set theory and cardinal arithmetic -- B Topology and Boolean algebras -- C Measure theory -- References -- Subject index -- Index of symbols.
,
English
Weitere Ausg.:
ISBN 0-521-09062-8
Weitere Ausg.:
ISBN 0-521-23487-5
Sprache:
Englisch
