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Proving the Banach–Alaoglu Theorem via the Existence of the Stone–Čech Compactification

Hossein Hosseini Giv
The American Mathematical Monthly
Vol. 121, No. 2 (February 2014), pp. 167-169
DOI: 10.4169/amer.math.monthly.121.02.167
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.02.167
Page Count: 3
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Proving the Banach–Alaoglu Theorem via the Existence of the Stone–Čech Compactification
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Abstract

Abstract The Banach–Alaoglu theorem is an important result in functional analysis whose standard proof relies on Tychonoff’s theorem. In this note, the theorem is proved by assuming the existence of the Stone–Čech compactification for completely regular topological spaces.

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