Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-06-01T03:01:24.283Z Has data issue: false hasContentIssue false
  • English
  • Français

A General Selection Principle, with Applications in Analysis and Algebra

Published online by Cambridge University Press:  20 November 2018

Norman M. Rice
Norman M. Rice*
Affiliation:
Queen's University, Kingston, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The General Selection Principle referred to in the title is really Tychonoff's theorem on products of compact spaces, but in a somewhat disguised form (c.f. Theorem 2.1, below). It is believed that this form is one which lends itself very well to many applications. More specifically, one of the immediate corollaries of the main theorem is a theorem due to Rado (c.f. Cor 2.1.1.), which has been used by Erdos and de Bruijn [2], Luxemburg [7], and the author [9] to give simple proofs of a variety of results.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 573 - 584
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bourbaki, N., Integration (Act. Se. et Ind. 1175, Hermann, Paris, 1952).Google Scholar
2. de Bruijn, N.G. and Erdos, P., A color problem for infinite graphs and a problem in the theory of relations, Nederl. Akad. Wetensch. (A) 54 (1951) 371-373.Google Scholar
3. Freudenthal, H., Teilweise geordnete Moduln, Proc. Acad. Sci. Amsterdam 39 (1936) 641-651.Google Scholar
4. Gottschalk, W. H., Choice Functions and Tychonoff's theorem, Proc. Amer. Math. Soc. 2 (1951) 172.Google Scholar
5. Halmos, P.R., Measure Theory (Van Nostrand, New York, 1950).Google Scholar
6. Kadison, R. V., A representation theory for commutative topological algebra, Memoirs Amer. Math. Soc. 7 (1951).Google Scholar
7. Luxemburg, W. A.J., A remark on a paper by N.G. de Bruijn and P. Erdos, Nederl. Akad. Wetensch. (A) 65 (1962) 343-345.Google Scholar
8. Rado, R., Axiomatic treatment of rank in infinite sets, Canad. J. Math. 1 (1949) 337-343.Google Scholar
9. Rice, N.M., Stone's representation theorem for Boolean algebras, Amer. Math. Monthly 6 (1968) 503-504.Google Scholar
10. Rice, N.M., Multiplication in vector lattices, Canad. J. Math., 20 (1968) 1136-1149.Google Scholar
11. Stone, M. H., The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936) 37-111.Google Scholar