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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
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.02.167
Page Count: 3
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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.
Copyright the Mathematical Association of America 2014