$X$ is a $K$-linear Banach space. $(X^*,\tau_{w^*})$ is metrizable $\iff$ X is Finite Dimensional.
A completely unrelated question:
What is the meaning of "the topology $\sigma(X,X^*)$"?
2026-04-05 22:36:24.1775428584
Metrizability of weak * topology of finite dimensional banach spaces
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