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

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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. 
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
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     title = {A {General} {Selection} {Principle,} with {Applications} in {Analysis} and {Algebra}},
     journal = {Canadian mathematical bulletin},
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     year = {1968},
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     number = {4},
     doi = {10.4153/CMB-1968-069-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-069-4/}
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