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- W4298472579 abstract "We prove that if an analytic subset $A$ of a linear metric space $X$ is not contained in a $sigma Z_omega$-subset of $X$ then for every Polish convex set $K$ with dense affine hull in $X$ the sum $A+K$ is non-meager in $X$ and the sets $A+A+K$ and $A-A+K$ have non-empty interior in the completion $bar X$ of $X$. This implies two results: (i) an analytic subgroup $A$ of a linear metric space $X$ is a $sigma Z_omega$-space if $A$ is not Polish and $A$ contains a Polish convex set $K$ with dense affine hull in $X$; (ii) a dense convex analytic subset $A$ of a linear metric space $X$ is a $sigma Z_omega$-space if $A$ contains no open Polish subspace and $A$ contains a Polish convex set $K$ with dense affine hull in $X$." @default.
- W4298472579 created "2022-10-02" @default.
- W4298472579 creator A5088614199 @default.
- W4298472579 date "2015-08-28" @default.
- W4298472579 modified "2023-09-25" @default.
- W4298472579 title "Detecting $sigma Z_n$-sets in topological groups and linear metric spaces" @default.
- W4298472579 doi "https://doi.org/10.48550/arxiv.1508.07297" @default.
- W4298472579 hasPublicationYear "2015" @default.
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