## Name for metric spaces with useful unique-ball-intersection property?

When dealing with the problem of extending a Lipschitz function f:A→Y between metric spaces across an inclusion A↪X, one often imposes (conditions which imply) the following property on the target space Y. I’d like to know if this property has a name. Let me describe our property: there exists a uniform bound d∈(0,∞) so that … Read more

## Terminology for filtered ∞\infty-categories

Often to prove that a simplicial set X∙ is a contractible ∞-groupoid, we instead prove that X∙ is a contractible Kan complex (i.e. satisfies the extension property for inclusions ∂Δn↪Δn), which is clearly a stronger property. I find myself in the situation of proving that a simplicial set X∙ is a filtered ∞-category by proving … Read more

## English language and Mathematics

I have a question maybe more relevant to an English language section of StackExchange, but I doubt that anybody but a Mathematician could properly answer my question. Let $\mathcal M$ be a smooth manifold, let $X$ be a smooth vector field on $\mathcal M$ and let $\Sigma$ be a smooth hypersurface of $\mathcal M$. Let … Read more

## Terminology for a foliation that is only tangentially smooth

I’d like to get some information and references, starting with a name, for the following quite common situation, for a smooth (i.e. C∞) n-manifold M. A partition L of M is given such that for any p∈M there is an open nbd U of p and a homeomorphism ϕ:Rk×Rn−k→U such that {L∩U:L∈L}={ϕ(Rk×{y}):y∈Rn−k} For all α=(α1,…,αk)∈Nk, … Read more

## Name for “étale-essential” properties

A map of rings f:A→B is called “essentially P” if there exists some A→C→B such that A→C has property P and C→B is a localization, that is to say, a filtered colimit of Zariski-open C-algebras. Is there a name for a map A→B such that there exists a factorization A→C→B such that A→C has property … Read more

## Is there a name for this slightly stronger version of Cesàro convergence which “more quickly ignores earlier terms”?

Let V be a normed vector space, let l∈V, and let (an) be a sequence in V. We say that an is Cesàro-convergent to l if 1n∑ni=1ai→l as n→∞. Now I will say that an is (∗)-convergent to l if for any unbounded increasing sequences of positive integers (mn) and (kn), we have 1mnkn+mn∑i=kn+1ai→l as n→∞. This … Read more