Uncountability of Hamel Basis for Banach Space

Last week, I was discussing with a student some elementary details of normed and Banach spaces. The subject of Hamel bases came up, and I incorrectly said that a Hamel basis for an infinite-dimensional normed space is necessarily uncountable. After thinking about the proof I had in mind, I realized that I needed the additional hypothesis of completeness. Here’s my proof, if you’re interested.

Advertisements
This entry was posted in math.FA and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s