MathOverflow

Let $0 < k < n$ be an integer and $K \subseteq \mathbf{R}^n$ be a compact set such that the Hausdorff measure $0< \mathscr{H}^k(K) < \infty$. Let $\mathscr{M}^{*k}$ denote the k-dimensional upper Minkowski content. Is it true that$$ ...

We endow $\newcommand{\Po}{{\mathcal P}(\omega)}\Po$ with a graph structure by letting$E = \big\{\{a,b\}: a, b\subseteq \omega \land a \neq b \land (\exists n\in \omega(a\cap b = \{n\})\big\}$.
Every clique of $(\Po, E)$ is at most countable, so the clique number is $\aleph_0$....

Let
$a(n)$ be an integer sequence with EGF $A(x)$ such that $$ A(x) = \frac{\exp(x)}{\cos(x)-\sin(x)}. $$
$T(n,k)$ be an integer coefficients such that $$ T(n,k) = T(n-1,k) + (k+1)T(n-1,k+1) + kT(n-1,k-1), \\ T(n,0) = T(n-1,0) + T(n-1,1), \\ T(0,k) = 1. $$...

In a discussion with Kevin Buzzard it arose that the adeles of $\mathbb{Q}$ are a Polish space, and before it was realised how easy this was to see (they are a locally compact Hausdorff second countable space), I was wondering if one could construct...