# Questions tagged [terminology]

Questions of the kind "What's the name for a X that satisfies property Y?"

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### Extremely disconnected or extremally disconnected?

In the context of Banach space theory, what is the correct terminology: extremally disconnected or extremely disconnected. Looking through the internet I have met using both extremely and extremally ...

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### Terminology: group action with normal stabilizers

This is just a terminology question. Is there a name for a group action which is transitive and for which the stabilizers are normal subgroups?
In this situation, the stabilizers are all equal. If the ...

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### Is there a more descriptive term for Characteristic Classes? [closed]

Recently I went along to a conference on Communication in Mathematics where a number of people, me amongst them, complained about talks where one only understood 5% of what was going on.
A part of ...

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### "Variable and fixed" in categories

We often find in Grothendieck terminology the words variable and fixed (or absolute).
For example in SGA 4 studies variable topological spaces, groups, and categories as examples of morphisms of topos....

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### Name for class of functions satisfying $E[f(X)] = f(E[X])$

If $X$ is a continuous random variable and $E[\cdot]$ denotes the expected value, then does the class of functions $f$ for which
$$
E[f(X)] = f(E[X])
$$
have a name? Obviously if $f$ is linear then ...

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### Planar graphs - more or less

A graph is planar if it can be drawn on the plane in such a way that its edges do not cross each other.
A graph is $k$-planar if it can be drawn on the plane in such a way that each of its edges is ...

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### Name of a space with both a topology and a metric that are not compatible?

Let $(X,\tau,d)$ be a space where $\tau$ is a topology and $d$ is a metric, where the topology $\tau$ is not necessarily compatible with $d$.
Is there a canonical name for such a structure (maybe ...

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### $n$-connected spaces (terminology)

A graph is called $n$-connected if it remains connected after removal $\le n$ vertices.
Question. What is the name of an analogous property of topological spaces: a space that remains connected after ...

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### So many types of subwords! How are they called?

Let $\mathscr F(X)$ be the free monoid on an alphabet $X$, the carrier set of $\mathscr F(X)$ being the union of $X^{\times k}$ (the Cartesian product of $k$ copies of $X$) as $k$ ranges over $\mathbb ...

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### What is the name for a point that is periodic to within $\varepsilon$?

Let $X$ be a set and $f: X \to X$ a function. A point $x \in X$ is, of course, said to be periodic for $f$ if $x \in \{f(x), f^2(x), \ldots\}$.
Now suppose that $X$ is a topological space and $f$ is ...

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### The formal name of extracting an element from a matrix, or from a p-dimensional kernel

Suppose $X=(X_1,...,X_p) \in (L^2(\mathcal{T}))^p$ and $\mathcal{K}=X\otimes X$. I want to define a mapping $\mathcal{A_{jk}}$ such that $\mathcal{A_{jk}}(\mathcal{K})=X_j\otimes X_k$.
I just wonder ...

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### Does the space of hyperplanes in the Grassmannian have a name?

A way of defining the Grassmannian $Gr(k,n)$ is to consider the space of $k\times n$ matrices mod $GL(k)$ transformations on the rows. I'm interested in the space of $k\times 2n$ matrices mod $GL(k)$ ...

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### Terminological question on finite groups

Is there a standard term to denote finite groups $G$ with the property that the projection $\operatorname{Aut} G \to \operatorname{Out} G$ from automorphisms of $G$ to outer automorphisms is split?

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### Name for closure property: set of maps closed under taking $(f,g)\mapsto (f-g)/2$

Suppose that $F$ is a collection of functions mapping some set $\Omega$ to $\mathbb{R}$, with the following closure property: whenever $f,g\in F$, we also have $(f-g)/2\in F$. Is there a name for this ...

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### Is there a name for the space of gradients?

Let $\Omega \subseteq \mathbb{R}^n$ be a bounded domain. Define the set
$$H = \left\{\nabla f : f \in \mathcal{C}^1(\Omega)\right\}.$$
I suspect that $H$ is a Hilbert space (though I am unsure about ...

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### Adjoint natural transformations

Is there a name for antiparallel natural transformations between ${\bf Cat}$-valued functors such that the components at each object form an adjunction?
That is, suppose we have functors $F,G:\...

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### Word combinatorics terminology question

I'm looking for the name of what I suspect must be a standard property, and also for a possible statement about that property.
First the property: $W=a_0\ldots a_{n-1}$ has this property if for all $1\...

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### Is there a name for the algebraic structure of all real matrices?

I know there are matrix rings, but what do we call the structure of the set of ALL real matrices, with the usual sum and product? We are looking for a kind of algebra whose operations aren't defined ...

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### Terminology for the property: "Each uncountable disjoint open family is locally countable"

Suppose that a topological space $X$ satisfies the following property
(P): "Each uncountable disjoint open family is locally countable",
where a family $\mathcal U$ of subsets of $X$ is ...

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### Terminology: maps which are bi-Lipschitz on compact subsets

Let $X$ and $Y$ be metric spaces and let $f:X\rightarrow Y$ be such that: for every compact subset $K$ of $X$ the restricted map $f|_K:K\rightarrow Y$ defined by $f|_K(x)=f(x)$ is bi-Lipschitz (with ...

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### A question on terminology for sequences satisfying $\gcd(a_m,a_n)=a_{\gcd(m,n)}$

How do you refer to those sequences $\{a_{n}\}_{n \in \mathbb{Z}^{+}}$ of integers that satisfy the condition $\text{gcd}(a_{m}, a_{n}) = a_{\text{gcd}(m,n)}$ for every $(m,n) \in \mathbb{Z}^{+} \...

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### What is the name for the construction of this poset related to coherence of degeneracies of the simplex category?

I present you a family of posets here. I don't say the posets themselves have a conventional name. However I'm sure the general construction of this kind has received some terminology, related to ...

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### Does this hexagon theorem have a name - Can I call is Viet Nam hexagon theorem?

Question : Do you know this property of a hexagon - Can I call is Viet Nam hexagon theorem?
Consider the configuration: Six points $A_1$, $A_2$, $A_3$, $A_4$, $A_5$, $A_6$ in a plane and let six ...

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### What do you call a scaled orthogonal map?

What do you call a linear map of the form $\alpha X$, where $\alpha\in\Bbb R$ and $X\in\mathrm O(V)$ is an orthogonal map ($V$ being some linear space with inner product)? Are there established names, ...

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### Terminology for the "natural probability measure" on the set of irreducible characters of a finite group

To be specific: if $G$ is a finite group and $\operatorname{Irr}(G)$ the set of its irreducible characters (over the complex field) then we know that
$$
1 = \sum_{\phi \in {\rm Irr}(G)} \frac{(d_\phi)^...

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### Writing the plane as {(x,y,z): x+y+z=0} [closed]

One can coordinatize the plane by choosing three axes at 120 degree angles and representing points by triples $(x,y,z)$ with $x+y+z=0$. Is there an accepted name for this kind of coordinate system? (...

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### What should you call a Mori Dream Space (or surface) in Spanish?

(My apologies if this turns out to be judged to be not appropriate for MathOverflow - I thought about it twice, but then I am nearly certain that I would be much less likely to get an answer there!)
&...

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### Great polyhedra: What does "great" signify?

Great Cubicuboctahedron
Great Icosacronic Hexecontahedron
Great Rhombic Triacontahedron
Great Snub Icosidodecahedron
Great Stellated Dodecahedron
Great Triakis Octahedron
...
There are many polyhedra ...

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### Functions with periodic sequence of derivative-values

Question:
is there an established name for the set $\Big\lbrace\ f {\Large\ \boldsymbol{|}}\ f\in C^\infty\quad {\Large\boldsymbol{\land}}\quad \exists\,{k\in\mathbb{N}^+}:\frac{d^{i+k}}{dx^{i+k}}f(x)=...

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### PCA terminology eigenspace / latent space

For PCA, it is quite confusing that the terms 'Eigenspace' and 'latent space' are often used interwoven or mixed and multiple researchers define them differently. From my understanding, there are two ...

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### Why is $H$ the standard notation for mean curvature?

I am curious about the origin of the notation $H$ to denote the mean curvature of a surface in $\mathbb{R}^{3}$.
I suppose that the symbol $K$, which is commonly used to denote the Gaussian curvature, ...

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### Terminology question

Let $K$ be a commutative ring with unit and suppose that $R$ is a ring that is a left $K$-module satisfying $c(rs)=(cr)s$ for all $c\in K$ and $r,s\in R$. We do not require that $r(cs)=c(rs)$ and so $...

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### Smallest relation in complement of partial order that prohibits its extension

Let $P$ be a partial order on a finite set $S$ (assume that every element is related to at least one other element besides itself…this raises a few quick questions: is this implied by the definition ...

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### Nomenclature for largest odd factor

Is there a standard phrase for the largest odd factor of a positive integer $n$, or more generally for $n$ divided by the largest power of $p$ that divides it (with $p$ some fixed prime)? Five minutes ...

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### Restricted sumsets - the origins?

The sumset of the subsets $A$ and $B$ of an additively written group is defined by $A+B:=\{a+b\colon a\in A,\ b\in B\}$. The basic idea to add sets has been around since Cauchy at least.
Erdős and ...

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### Has this "optimal constrained transport" notion of convergence of measures been named and/or studied?

Let $(X,d)$ be a compact metric space, and let $\{\mu_n\}_{n \in \mathbb{N} \cup \{\infty\}}$ be a family of Borel probability measures on $X$.
Fix $L \geq 1$. I will say that $\mu_n$ converges in ...

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### Is there a proper term for a "continuum-convex" set?

Let $X$ be a Banach space, and for any compactly supported Borel probability measure $\mathbb{P}$ on $X$, define the mean $\mu_\mathbb{P}$ by $\mu_\mathbb{P}=\int_X x \, \mathbb{P}(dx)$.
I want to say ...

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### Terminology "upper" Ahlfors regular measure

Let $(X,d)$ be a metric space and $m$ be a Borel measure on $(X,d)$. The measure $m$ is called Ahlors regular if $m(B(x,r))\asymp r^q$ for some $q>0$ and each $x\in X$. Is there a name for ...

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### Almost exactness - terminology

Consider a sequence of (torsion-free) abelian groups
\begin{equation*}
\dots\stackrel{p}{\longrightarrow} G\stackrel{q}{\longrightarrow}\dots
\end{equation*}
with the property
\begin{equation*}
\text{...

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### Name of the "s" parameter in Ungar's theory of hyperbolic geometry

I have done a R package which implements Ungar's approach to hyperbolic geometry, for the hyperboloid model. In this theory, there is a parameter $s>0$ which controls the curvature of the ...

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### Name for function projecting a 3D point to the surface of aligned sphere

Let there be a 3D point $\mathbf{P} = \begin{bmatrix} X & Y & Z\end{bmatrix}^{\top}$ and a sphere $\mathcal{S}$ with radius $r$ and centroid at the origin, everything expressed w.r.t the same ...

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### Expectation value of inverse covariance matrix when sampling from unit sphere

Let $X \sim \operatorname{Unif}S_{d-1}$, so $X\in\mathbb{R}^d$ and is distributed uniformly on the unit sphere.
Then let $X_1, \dots, X_n \sim X$ iid and define the matrix $\mathbf{X}\in\mathbb{R}^{n\...

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### Terminology for the parts of composition?

In function composition, binary relation composition, or more generally category theory, are there distinct names for the two things being composed?
If we have $f:X \rightarrow Y$ and $g:Y \rightarrow ...

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### What is the name of this relative semidirect product of groups?

We have two well known definitions of the semidirect product $N \rtimes H$ of groups:
(Internal semidirect product) We write $G = N \rtimes H$ if $N$ is a normal subgroup of $G$, $H$ is another ...

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### Direct and inverse image terminology

Let $f\colon X\to Y$ be a continuous map. Then $f$ induces a geometric morphism $f^\ast\dashv f_\ast\colon \mathrm{Sh}(X)\leftrightarrows\mathrm{Sh}(Y)$, whose left adjoint is called inverse image and ...

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### Dart of a graph

I want to understand the Dart of a graph. Many authors and also in the book Graphs on surfaces and their applications by Sergei K. Lando, Alexander K. Zvonkin used this term Dart of a Graph/edges. I ...

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### What is the term for two figures being congruent and of same orientation?

In the plane, two figures are called congruent exactly if one can be transformed into the other by translation, rotation, and reflection. What if reflection is excluded, that is, preservation of ...

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### Selectively countable Boolean algebras of sets (terminology)

I am interested in the name for the following property of a Boolean algebra $\mathcal A$ of subsets of a set $X$:
$(\star)$ for any sequence $(A_n)_{n\in\omega}$ of pairwise disjoint nonempty sets in $...

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### Partitions that are "mutually nested"

Let $\mathcal{P}_1,\dots,\mathcal{P}_m$ be a collection of ordered $n$-partitions of a set $\mathcal S$, which is to say that that $$\mathcal{P}_i = \{P^i_1\cup\dots\cup P^i_n\}$$ for all $i$. ...

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### Do these distributions have a name already?

In playing with some math finance stuff I ran into the following distribution and I was curious if someone had a name for it or has studied it or worked with it already.
To start, let $\Delta^n$ be ...