Dear friends, I am used to the definition of relative sequential compactness of ##X'##, a subset of a topological space ##X##, as(adsbygoogle = window.adsbygoogle || []).push({}); every sequence in ##X'## has a subsequence converging to a point in##X##.

I know that if ##E## is a separable Banach space then every weak##^{\ast}##-compact subset of ##E^{\ast}## is sequentially weak##^{\ast}##-compact and it seems to me that such an assertion can be generalised to "if ##E## is a separable Banach space then every relatively weak##^{\ast}##-compact subset of ##E^{\ast}## is relatively sequentially weak##^{\ast}##-compact".

Have I correctly desumed this generalisation?

I ##\infty##-ly thank you for any help!

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# Definition of relative sequential compactness

Can you offer guidance or do you also need help?

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