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What is the smallest number of hyperplanes covering $\ell_2$?

For a Banach space $X\ne \{0\}$, let $\mathrm{cov}_H(X)$ be the smallest number of hyperplanes covering $X$. By a hyperplane in a Banach space I understand any closed affine subspace of codimension ...
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What is the smallest number of nowhere dense affine subsets covering a topological group?

$\DeclareMathOperator\cov{cov}\newcommand\A{\text A}$A subset $A$ of a group $G$ is called affine if $A=xHy$ for some subgroup $H\subseteq G$ and some $x,y\in G$. Given a non-discrete topological ...
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