Welcome to mathimatikoi.org forum; Enjoy your visit here.

A Classic Result

Linear Algebra, Algebraic structures (Groups, Rings, Modules, etc), Galois theory, Homological Algebra
Post Reply
Tsakanikas Nickos
Community Team
Community Team
Articles: 0
Posts: 314
Joined: Tue Nov 10, 2015 8:25 pm

A Classic Result

#1

Post by Tsakanikas Nickos » 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.
Post Reply