A Classic Result

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
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Tsakanikas Nickos
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Joined: Tue Nov 10, 2015 8:25 pm

A Classic Result

#1

Post by Tsakanikas Nickos »

Show that any vector space \( \displaystyle V \) over a field \( \displaystyle \mathbb{K} \) has a (Hamel) basis.

Furthermore, show that any two bases of \( \displaystyle V \) have the same cardinality.

Additionally, show that if \( \displaystyle X \) is an infinite dimensional Banach space, then every Hamel basis of \( \displaystyle X \) is uncountable.
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