7 Matching Annotations
 Apr 2023

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5

1.
A finite dimensional spaces/subspaces have equivalence between compactness and Closed and Bounded. In this case, we infinite dimensions. Then there is some closed and bounded spaces that is not compact.
That was my first thought that is all.

12.
From 11, we have: 1. Norm implies convex norm ball.
Hence the contra positive of the statement will state that, if the norm ball is not convex, then it's not a norm.

11. (Convex set, segment)
Unit Ball in a Normed space is convex

 Mar 2023

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