5 problems

Finite-power strong measure zero conjecture. If $X$ has strong measure zero and $|X|<\mathfrak{b}$, then all finite powers of $X$ have strong measure zero.

Let $X$ be a set of reals with strong measure zero, and suppose that $|X|<\mathfrak{b}$, where $\mathfrak{b}$ is the bounding number. A finite power of $X$ is a Cartesian product…

For a Polish group $\mathbb{G}$, define … Also let $\operatorname{non}(\operatorname{Smz}(\mathbb{G}))$ be the least cardinality of a subset of $\mathbb{G}$ that is not of strong m…

Let $\mathbb{G}$ be a Polish group. A nonempty subset $C\subseteq\mathbb{G}$ is anti-GMS if it is nowhere dense and, for every sequence $\{U_n:n\in\omega\}$ of open neighborhoods o…

Let $\mathbb{G}$ be a Polish group. A set $S\subseteq\mathbb{G}$ is of strong measure zero, and a set $M\subseteq\mathbb{G}$ is meager. Galvin–Mycielski–Solovay characterization co…