Tychonoff Theorem
المؤلف:
Kelley, J. L.
المصدر:
"The Tychonoff Product Theorem Implies the Axiom of Choice." Fund. Math. 37
الجزء والصفحة:
75-76
3-6-2021
1959
Tychonoff Theorem
A product space 
is compact iff 
is compact for all 
. In other words, the topological product of any number of compact spaces is compact. In particular, compactness is a productive property. As a consequence, every Hilbert cube is compact.
This statement implies the axiom of choice, as proven by Kelley (1950).
REFERENCES:
Kelley, J. L. "The Tychonoff Product Theorem Implies the Axiom of Choice." Fund. Math. 37, 75-76, 1950.
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