Hi!

I have been struggling with an proof for days now and would like to see if there is someone in here who can help me out.

the excersise is as follows;

We have a Banach Space A. Let {e_alpha}_(alpha belongs to A) be a base when A is considered being a linear space and show with Baires category theorem that the index set A is either finite or not countable?

Someone who is indulged to try?

Peter