Chain conditions in topology
著者
書誌事項
Chain conditions in topology
（Cambridge tracts in mathematics and mathematical physics, 79）
Cambridge University Press, 2008, c1982
- : pbk
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注記
"This digitally printed version 2008"--T.p. verso
Includes bibliographical references and index
内容説明・目次
内容説明
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. Erdoes and the Hungarian school, by Erdoes 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.
目次
- 1. Some infinitary combinatorics
- 2. Introducing the chain conditions
- 3. Chain conditions in products
- 4. Classes of calibres, using -products
- 5. Calibres of compact spaces
- 6. Strictly positive measures
- 7. Between property (K) and the countable chain condition
- 8. Classes of compact-calibres, using spaces of ultralilters
- 9. Pseudo-compactness numbers: examples
- 10. Continuous functions on product spaces.
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