Is it a unity norm, closed sphere, in lp, (not Lp ), compact ? I hear that it is not !! Is there a counterexample for this or a proof ? Thanks a lot !
2026-03-30 05:28:55.1774848535
On the question of lp compactness. Counterxamples
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Spheres in an infinite-dimensional Banach space are never compact.
In this case it's easy to find a sequence of points in the sphere with distance $\ge 1$ between them.