Questions on the usage and meaning of words in mathematics, the names for mathematical entities, and other such questions.

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9
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150 views

Official name(s) for a certain type of p-group

I'm implementing a class of groups into Sage (sagemath.org), a computer algebra system, and I'm wondering if it has any official names. I found it in Gorenstein's "Finite Groups." It is there called ...
8
votes
0answers
56 views

Is there a name for the class of functions which are infinitely integrable in elementary functions?

Is there a name for the class of functions which are infinitely integrable in elementary functions, that is whose consecutive integrals also elementary not depending on how much times we took the ...
8
votes
0answers
116 views

Why are parabolic subgroups called “parabolic” subgroups?

I used to think that things called "parabolic" must have something to do with parabolas or their defining quadratic equations. In fact, terms like parabolic coordinate, parabolic partial differential ...
7
votes
0answers
91 views

Analogue of the term 'summand' for unions and intersections.

If we have a sum $\sum\limits_{i=1}^na_i$, we call the terms $a_i$ summands. In fact, in the cases of addition, subtraction, multiplication, and division, we have a large vocabulary to describe the ...
7
votes
0answers
121 views

Urysohn's Lemma needn't hold in the absence of choice. Alternate terminology for inequivalent definitions of “normal” spaces?

A topological space $\langle X,\tau\rangle$ is said to be normal if any two disjoint closed subsets are separated by open sets, meaning that for disjoint $E,F\subseteq X$ with $X\setminus E,X\setminus ...
7
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0answers
134 views

French translation of “well-powered” category

In order to write a report, I'm looking for a French translation of the term "well-powered category". Does anyone know the canonical term in French?
6
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0answers
70 views

Origins of the name “Q” and “R” for cofibrant and fibrant replacement functors.

In a model category $\mathscr M$ (in the modern sense, i.e. closed and with functorial factorizations), there is a notion of fibrant and cofibrant replacement functors. Specifically, for any object ...
6
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0answers
232 views

Is the kernel of any ring homomorphism a subring, according to this definition?

This is an exercise taken verbatim from Birkhoff and MacLane, A Survey of Modern Algebra: Show that if $\phi: R \rightarrow R'$ is any homomorphism of rings, then the set $K$ of those elements in ...
6
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172 views

'Galois Resolvent' and elementary symmetric polynomials in a paper by Noether

In Emmy Noether's 1915 paper "Der Endlichkeitssatz der Invarianten endlicher Gruppen", I saw the notion of a 'Galois resolvent', which I don't quite understand. Google didn't really help me with that, ...
5
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0answers
35 views

Is the definition of stabilizer given at Planet Math really the currently accepted definition among group theorists?

According to Planet Math, given a group $G$ a set $X$ a subset $S \subseteq X$ and a group action $G \times X \rightarrow X,$ then the stabilizer of $S$ is define to be: $\{g \in G \mid gS ...
5
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0answers
32 views

Name for Number of Ancestors/Descendants of Vertex in Directed Acyclic Graph

Let $G = (V, E)$ be a directed acyclic graph. For each vertex $v \in V$, define the ancestors of $v$ to be the set of vertices $u \in V$ such that there exists a directed path from $u$ to $v$. ...
5
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29 views

“Advective”, “diffusive”, “dispersive”, and related terms in the realm of PDEs

Whenever I read a paper involving PDEs, the discussion inevitably refers to “the dispersive term” or “the advective term” or similar. From context it is usually possible to figure out the antecedent, ...
5
votes
0answers
46 views

Is there a name for the algebra of substructures?

Let $X$ denote an entropic algebra (see here), which just means that all the operations of $X$ are homomorphisms $X^n \rightarrow X.$ Abelian groups are the classic example. Then for any operation of ...
5
votes
0answers
130 views

Why are they called orbits?

When we study actions in group theory, we consider sets of the form $$\text{Orb}_G(x)=\{gx\mid g\in G\} $$ that are called orbits. Although, the only reason I find convincing for that name is that in ...
5
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0answers
100 views

The counted is to the countable as the ??? is to the (order)-isomorphic.

We sometimes need to distinguish the counted from the countable. A counted set is a set equipped with a particular bijection into (some of) the natural numbers; a set is countable if there exists such ...
5
votes
0answers
74 views

Is there a standard name for the relation $X \times Y$?

Given sets $X$ and $Y$, is there a standard name for the relation $f : X \rightarrow Y$ whose graph equals $X \times Y$? Something like the full/maximum/top/total/complete relation?
5
votes
0answers
82 views

Topological Space in which every compact subset is metrizable

Is there an (more or less) established name for the class of topological spaces in which every compact subset is metrizable? This is true for example in (LF)-spaces (inductive limits of ...
5
votes
0answers
261 views

When are two objects essentially the same?

From the comments to this question I have learned, that many (most?) mathematicians are not very interested in the relationship between an object $X$ and its "correspondent" $F(X)$ for an arbitrary ...
5
votes
0answers
195 views

Does this property of scattered spaces have a name?

Let $K$ be a (Hausdorff) scattered topological space and for each ordinal $\alpha$ denote by $K^{(\alpha)}$ the $\alpha$th derivative of $K$ by the Cantor-Bendixson derivation (i.e., define ...
5
votes
0answers
201 views

Is there some official name for this function?

$$\sqrt{1 - (-1 + x\bmod 2)^2}\cdot\operatorname{sign}(-2 + x\bmod 4)$$ Like half-circles connected to each other to look like waves: Its plot looks smooth, but the function is actually not ...
4
votes
0answers
71 views

Is there a name for graphs with the following property?

The property of the graph is the following: For any vertex, there is a hamiltonian path starting with this vertex, but the graph is not hamiltonian. The following graph is a small example: ...
4
votes
0answers
48 views

Name for a body that can be completely described using its silhouettes

I'm shooting blind over here because I have no background in this field of mathematics. I assume that if you have a body (in $\mathbb{R}^3$), you can call it convex if any segment from one point ...
4
votes
0answers
88 views

“diverges to $1$”

$\newcommand{\logit}{\operatorname{logit}}$ A series may "diverge to $\infty$" or "diverge to $-\infty$"; a product may "diverge to $\infty$" or "diverge to $0$". postscript in response to comments: ...
4
votes
0answers
32 views

Subsets of cyclic group with distinct pairwise differences

Given a number $m\in\mathbb N$, let $\mathbb Z_m=\{0,1,\dots,m-1\}$ denote the ring of integers modulo $m$ (although we won't need multiplication, so any cyclic group of order $m$ will do). Given a ...
4
votes
0answers
52 views

Is there a name for a “rigid” sheaf?

Is there a name for the property of a sheaf $\mathcal F$ such that the restriction maps $\mathcal F(V) \to \mathcal F(U)$ are injective when $V$ is a connected open and $U$ is a nonempty open? In ...
4
votes
0answers
192 views

Difference between elementary submodel and elementary substructure

This is a really "elementary" question, forgive the pun. What is the difference between an elementary submodel and an elementary substructure (in first-order Logic)? Sincere thanks for help.
4
votes
0answers
63 views

What is the name of the function that indexes Grothendieck universes?

Assume Tarski-Grothendieck set theory. Then Grothendieck universes form a well-ordered proper class, so we can let $U_\alpha$ denote the $\alpha$'th Grothendieck universe, where $\alpha$ is an ...
4
votes
0answers
94 views

Has this function a name?

Has this function a name? $$f(x) = \prod_{i=2}^{\lceil \frac{x}{2} \rceil} \sin\left( \frac {\pi x}{i}\right)$$ (the product of $\sin( \frac {\pi x}{i})$ for $i=2,3,...,\lceil x/2 \rceil$)
4
votes
0answers
142 views

Terminology Question: Precompose vs Compose?

I was wondering if there was a standard convention on what 'precompose' means compared to 'compose', as I am often confused between the two when all sorts of text casually use both terminologies. For ...
4
votes
0answers
352 views

What is a bridgeless undirected planar 3-regular bipartite graph?

Draks asked a question about a sentence in Wikipedia stating that such-and-such (NP-hardness of Hamiltonian path detection) is true for "bridgeless undirected planar 3-regular bipartite graphs". What ...
4
votes
0answers
26 views

Terminology: how to call the compact version of an affine space?

How should I call briefly the space $M$, which is obtained when "forgetting" the origin (i.e. the identity) of an $n$-dimensional torus $T$ (i.e. $T$ is a compact $n$-dimensional abelian Lie group)? ...
4
votes
0answers
107 views

How do you call functions that fulfill $f(x)=\pm f(\pm 1/x)$?

A function $f(x)$ that fulfills $f(x)=\pm f(-x)$ is called (a)symmetric even/odd. How do you call functions that fulfill $f(x)=\color{blue}\pm f(\color{red}\pm 1/x)$? ...
4
votes
0answers
212 views

What does “toy-contour” mean?

When I reading Complex Analysis written by Elias M. Stein. In Chapter 2, he had introduced a notion "toy contour "without explaining. what does this exactly mean?
4
votes
0answers
67 views

What is the term used for space of analytic functions?

I deal with analytic functions in the unit disc represented as the series $\sum_{n=0}^\infty u_n z^n$, where the coefficients $u_n$ satisfy the condition $\sum_{n=0}^\infty n^\alpha|u_n| < \infty$ ...
4
votes
0answers
76 views

Terminology: functions on lattices

is there a name for the class of functions $f: L\times L \rightarrow L$, where $L$ is a lattice and $L\times L$ is the product lattice (ordered pointwise), with the following property: $f(x,y)=f( x ...
4
votes
0answers
49 views

Name of principal root function modified to return real values if possible

Is there a concise name for the function $f_n(x)\colon\mathbb{C}\to\mathbb{C}$ which returns the principal $n$th root of $x$, except in the case when $n$ is odd and $x$ is a negative real number, in ...
4
votes
0answers
203 views

Terminology for weighted projective spaces

For a sequence of positive integers $a_1, \ldots, a_n$ and a base ring $R$ there is a graded ring $R[x_1,\ldots, x_n]$ where $x_i$ is in degree $a_i$. We can then apply Proj and get a scheme, and ...
3
votes
0answers
45 views

Objects without extensions

How do you call an object $X$ for which every monomorphism $i : X \hookrightarrow Y$ has a retract (i.e.\ a morphism $r : Y \rightarrow X$ such that $r \cdot i = 1_X$)? I think of Y as an extension ...
3
votes
0answers
23 views

Is there a name for this partial order between metrics?

Suppose we have a set $X$ and two metrics $d_1,d_2$ on it (which may or may not attain $\infty$). Assume furthermore that $d_1,d_2$ have the same metric components (where a metric comoponent is a ...
3
votes
0answers
83 views

What is this method of dividing a plane called?

I have an idea of a method for recursively dividing a plane, and as I'd like to do more research about this algorithm and the set of points that it produces, I'd like to know what it's formally known ...
3
votes
0answers
26 views

How to call this homomorphism-like property?

In my communication theory work I derived a property that is essentially \begin{align} f(x)\cdot f(y) = f(x-y) \cdot A^N \end{align} where $A^N$ is some quantity from the technical context that is ...
3
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0answers
30 views

Terminology Regarding Basic Properties of Functions

Is there a cultural difference between saying that a function is 1-to-1 or injective, onto or surjective and a 1-to-1 correspondence or bijective?
3
votes
0answers
46 views

In complex analysis, is there a special name for functions that can be written as an infinite product of linear factors?

Let $Z$ denote a subset of $\mathbb{C}$. Then some functions $f : Z \rightarrow \mathbb{C}$ have the property that there exist sequences $a,b : \mathbb{N} \rightarrow \mathbb{C}$ such that for all $z ...
3
votes
0answers
95 views

“clopen” terminology: acceptable?

I like the term "clopen" (a set which is both open and closed in a topological space), though an instructor of mine hated it when I used it recently. (Approximately, "never, ever use that again.") Is ...
3
votes
0answers
77 views

Etymology of the term “weight vector”

I am writing a work on the representation theory of $SU(3)$ in basque and I would like to know the etymology of the term $\textbf{weight vector}$ in order to properly translate it.
3
votes
0answers
87 views

Why tensors are called tensors and how this relates to the rigorous definition?

The algebraic motivation for tensors is fairly good: we know how to deal with linear maps, we must deal with multilinear maps, so we want to reduce them to linear maps. The name tensor however seems ...
3
votes
0answers
36 views

Origin of the terminology “connected algebra”

I was wondering what is the origin of the word "connected" for a connected algebra ? To be more precise, why is a graded $R$-algebra $A_{\ast}$ with an augmentation $A_{\ast} \to R$ that restricts to ...
3
votes
0answers
51 views

Curve of centers of curvature

I really can't find the English name of the curve of the centers of curvature of a curve. Formulated more precisely: Suppose $\alpha$ is a regular curve in $\mathbb{E}^2$ and $||\alpha(t)'||=1$. How ...
3
votes
0answers
68 views

Is there a name for the following property in the theory of topological spaces?

I worked out the following lines. Probably it is totally trivial, but maybe this is interesting in the theory of topological/metric spaces. Let $\Omega$ be an open subset of the Euclidean $n$-space. ...
3
votes
0answers
42 views

Is there a name for subtracting a set of values from their max?

I hope this question is appropriate here - if it isn't let me know and I will remove it. I am wondering if there is a verb for the following operation: given a set of non-negative numbers, I take ...