Geodesic
A Theorem on Nets
Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 343-346

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DOI

It is well-known that Tychonoff's theorem on the product of compact spaces may be proved, for the special case of a countable number of metric spaces X1, X2..., Xn,..., in the following simple manner. 
Shimrat, M. A Theorem on Nets. Canadian mathematical bulletin, Tome 9 (1966) no. 3, pp. 343-346. doi: 10.4153/CMB-1966-042-x
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     title = {A {Theorem} on {Nets}},
     journal = {Canadian mathematical bulletin},
     pages = {343--346},
     year = {1966},
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     number = {3},
     doi = {10.4153/CMB-1966-042-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-042-x/}
}
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