Unit vectors in locally convex spaces

Question

Are there unit vectors in locally convex spaces. If yes, how can vectors be normalised in locally convex spaces?

score 2 · Answer 1 · answered Aug 14 '15 at 10:27

2

No. A locally convex space only has a topology given by a family of semi-norms. There is no canonical way to "normalize" a vector.

answered Aug 14 '15 at 10:27

Jochen

1 Answers1