Is it a fact that in an infinite dimensional normed linear space, the closed unit ball is never compact?(adsbygoogle = window.adsbygoogle || []).push({});

If so, how does one go about seeing this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Compactness of the unit ball in infinite dimension

**Physics Forums | Science Articles, Homework Help, Discussion**