I'm wondering if it is generally true that for any separable Banach space $X$ the space of linear, continuous functionals $X^*$ equipped with the $w^*$-topology is second countable. If so, how can I see this?
2026-03-25 20:09:50.1774469390
$X^*$ with $w^*$-topology second countable for separable Banach space $X$?
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