Chain Conditions in Topology

A chain condition is a property, typically involving considerations of cardinality, of the family of open subsets of a topological space.

W. W. Comfort (Author), S. Negrepontis (Author)

9780521090629, Cambridge University Press

Paperback / softback, published 27 November 2008

316 pages
21.6 x 14 x 1.8 cm, 0.4 kg

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.

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.

Subject Areas: Analytic topology [PBPH]