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

Is there any accepted single-word that means “partial function”?

When I’m explaining things involving partial functions, I usually end up stumbling over my words, like so: “Suppose $f : A \rightarrow B$ is a function, uhh, sorry I mean a partial function, and suppose $S$ denotes its support. Then there’s a corresponding restriction function… um, well, really its a partial function, $\overline{S} : A … Read more

What is the definition of “geometric analysis”? [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 4 years ago. Improve this question Recently it has been brought to my attention that the subject “geometric analysis” is not even well-defined (unlike the subject … Read more

Monads which are monoidal and opmonoidal

Do monads which are monoidal and opmonoidal have a name? (Bimonoidal?) In case they have already been studied, who can point me to a reference? More in detail. Let $(C,\otimes)$ be a symmetric (or braided) monoidal category. Let $(T,\eta,\mu)$ be a monad on $C$ such that: $T:C\to C$ is a bilax monoidal functor (compatible lax … Read more

Name for facet of a cone containing all but one edge

Let $C \subseteq \mathbb R^n$ be a polyhedral cone, so generated by its edges ($1$-dimensional faces) and $F \subseteq C$ a facet (codimension $1$ face) of it containing every edge except $e$. In particular, the map $F \times e \stackrel{+}{\to} C$ is an isomorphism of cones. Is there a name for this property of $F$ … 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