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YCor
YCor
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YCor
YCor
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Topological Vector Space A topological vector space $X$ is separable if its dual space $X^*$ is separable?

Let $(X,\tau)$ be a Topological Vector Spacetopological vector space such that the associated dual space $X^*$ is separable. Can we say that $X$ is separable ?

I know that this property is valid for Banach spaces but for topological vector spaces, I have no idea.

An idea please.

Topological Vector Space $X$ is separable if its dual space $X^*$ is separable?

Let $(X,\tau)$ be a Topological Vector Space such that the associated dual space $X^*$ is separable. Can we say that $X$ is separable ?

I know that this property is valid for Banach spaces but for topological vector spaces, I have no idea.

An idea please.

A topological vector space $X$ is separable if its dual space $X^*$ is separable?

Let $(X,\tau)$ be a topological vector space such that the associated dual space $X^*$ is separable. Can we say that $X$ is separable ?

I know that this property is valid for Banach spaces but for topological vector spaces, I have no idea.

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John nany
John nany
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Topological Vector Space $X$ is separable if its dual space $X^*$ is separable?

Let $(X,\tau)$ be a Topological Vector Space such that the associated dual space $X^*$ is separable. Can we say that $X$ is separable ?

I know that this property is valid for Banach spaces but for topological vector spaces, I have no idea.

An idea please.