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Weak *-topology of $X^*$ is metrizable if and only if …

Define metrizability weak*-topology of $X^*$ which $X$ is T.V.S on which $X^*$ separates points.

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    @RobertIsrael: You're right, I was mistaken.2012-05-20

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A topology on $X$ is metrizable if there is a metric on $X$ which produces the same topology.