In a Banach space,
is every compact set weakly compact set?
I guess its true just want to make sure.
Thank you!!
2026-03-26 23:06:16.1774566376
Compact and weakly compact
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The weak topology is coarser than the strong topology, therefore strong-compact subsets are weak-compact.
This is a purely topological fact: every cover by open sets from the coarser topology is a cover by open sets from the finer topology, and therefore a finite subcover exists a fortiori.