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yada
yada
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Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger Polish topology under which $X$ is a topological vector space or even locally convex?

Similarly, if $X$ is a Souslin vector space topology then it is knownknown (p. 4) that there exists a stronger Souslin metrizable topology. Does there also exist a stronger Souslin metrizable vector space topology?

Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger Polish topology under which $X$ is a topological vector space or even locally convex?

Similarly, if $X$ is a Souslin vector space topology then it is known that there exists a stronger Souslin metrizable topology. Does there also exist a stronger Souslin metrizable vector space topology?

Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger Polish topology under which $X$ is a topological vector space or even locally convex?

Similarly, if $X$ is a Souslin vector space topology then it is known (p. 4) that there exists a stronger Souslin metrizable topology. Does there also exist a stronger Souslin metrizable vector space topology?

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Pietro Majer
Pietro Majer
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Does Has every Lusin vector space has a stronger Polish vector space topology?

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yada
yada
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  • 11
  • 19

Does every Lusin vector space has a stronger Polish vector space topology?

Let $X$ be a topological vector space or even a locally convex space such that its (vector space) topology is Lusin, i.e. there is some stronger Polish topology. Does there also exist a stronger Polish topology under which $X$ is a topological vector space or even locally convex?

Similarly, if $X$ is a Souslin vector space topology then it is known that there exists a stronger Souslin metrizable topology. Does there also exist a stronger Souslin metrizable vector space topology?