MathOverflow

I am a student studying higher topos theory and categorical quantum mechanics. As a learning exercise, I constructed an explicit model of a cohesive linear ∞-topos – an ∞-topos equipped with a cohesive adjoint triple (Π, ♭, ♯) and an idempotent product...

A finite, undirected graph $G=(V,E)$ is connected in the traditional sense if for all $v, w\in V$ with $v\neq w$ there is a finite path from $v$ to $w$.
Moreover, $G$ is connected in the topological sense if whenever $S\subseteq V$ is nonempty with $S \neq V$, then there is $e\in E$ such that $e\cap S\neq \varnothing $ and $e\setminus S\neq \varnothing$ (i.e., $S$ contains exactly $1$ element from the...

Assume $\Gamma$ is an infinite set composed of terms (of finite length), and $A$ is a term (of finite length). For example, $\Gamma=\{x,y\sqcup z,x_1,x_2,x_3,\cdots\}$, $A=(x\sqcap y)\sqcup(x\sqcap z)$. Obviously, $\mathop⨅\Gamma\le A$ holds in any of...

Please, help me find connections between two types of convergence:
Let $\{X_n\}_{n\ge1}: (\Omega,F,P) \rightarrow (\mathbb{R},Bor)$ be a sequence of r.v., there are two convergences:
1) $X_n \rightarrow X \hspace{0.2cm}(sLip)$, i.e. $\sum_{n\ge1} E|f(X_n) - f(X)| < \infty \hspace{0.2cm}\forall f \in Lip$ and bounded...