Geodesic
A General Selection Principle, with Applications in Analysis and Algebra
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 573-584

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Rice, Norman M. A General Selection Principle, with Applications in Analysis and Algebra. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 573-584. doi: 10.4153/CMB-1968-069-4
@article{10_4153_CMB_1968_069_4,
     author = {Rice, Norman M.},
     title = {A {General} {Selection} {Principle,} with {Applications} in {Analysis} and {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {573--584},
     year = {1968},
     volume = {11},
     number = {4},
     doi = {10.4153/CMB-1968-069-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-069-4/}
}
TY  - JOUR
AU  - Rice, Norman M.
TI  - A General Selection Principle, with Applications in Analysis and Algebra
JO  - Canadian mathematical bulletin
PY  - 1968
SP  - 573
EP  - 584
VL  - 11
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-069-4/
DO  - 10.4153/CMB-1968-069-4
ID  - 10_4153_CMB_1968_069_4
ER  - 
%0 Journal Article
%A Rice, Norman M.
%T A General Selection Principle, with Applications in Analysis and Algebra
%J Canadian mathematical bulletin
%D 1968
%P 573-584
%V 11
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-069-4/
%R 10.4153/CMB-1968-069-4
%F 10_4153_CMB_1968_069_4

[1] 1. Bourbaki, N., Integration (Act. Se. et Ind. 1175, Hermann, Paris, 1952). Google Scholar

[2] 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] 3. Freudenthal, H., Teilweise geordnete Moduln, Proc. Acad. Sci. Amsterdam 39 (1936) 641-651. Google Scholar

[4] 4. Gottschalk, W. H., Choice Functions and Tychonoff's theorem, Proc. Amer. Math. Soc. 2 (1951) 172. Google Scholar

[5] 5. Halmos, P.R., Measure Theory (Van Nostrand, New York, 1950). Google Scholar

[6] 6. Kadison, R. V., A representation theory for commutative topological algebra, Memoirs Amer. Math. Soc. 7 (1951). Google Scholar

[7] 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] 8. Rado, R., Axiomatic treatment of rank in infinite sets, Canad. J. Math. 1 (1949) 337-343. Google Scholar

[9] 9. Rice, N.M., Stone's representation theorem for Boolean algebras, Amer. Math. Monthly 6 (1968) 503-504. Google Scholar

[10] 10. Rice, N.M., Multiplication in vector lattices, Canad. J. Math., 20 (1968) 1136-1149. Google Scholar

[11] 11. Stone, M. H., The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936) 37-111. Google Scholar

Cité par Sources :