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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
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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

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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