A Classic Result
Posted: Mon Jan 18, 2016 4:06 am
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.
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.