All Questions

Call a finite subset $S$ of the plane with an even number of points an odd Jackson set, if there is an $A\subset \mathbb R^2$ such that $A$ meets every congruent copy of $S$ in an odd number of points....

Is there a nonempty planar set that contains $0$ or $2$ vertices from each unit equilateral triangle? I know that such a set cannot be measurable. In fact, my motivation is to extend a Falconer-Croft ...

Suppose we are given two sets, $S$ and $A$ in the plane, such that $S$ is finite, with a special point, $s_0$, while neither $A$ nor its complement is a null-set, i.e., the outer Lebesgue measure of $...

Let us say a metric probability space $(X,\rho,\mu)$ has property (*) if: the support of $\mu$ is contained in a separable subspace of $X$. Questions: 1. Is there a standard name for this property? ...

Let $G=(V, E)$ be the following graph: $V=\ell^\infty = $ set of bounded real sequences, with the norm $$\|x\|_\infty = \sup_{n\in\mathbb{N}}|x_n|,$$ $E = \big\{\{x,y\}: x,y\in \ell^\infty \text{ and ...