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

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13
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126 views

Name for a ring that also has composition - aka function application?

What is the following type of ring? Does it have a name? Suppose $(R,\cdot,+,0,1)$ is a ring with another binary operation, $\circ$ with the properties: $$(a\circ b)\circ c=a\circ(b\circ c)\\ ...
12
votes
0answers
151 views

How to name these “ideals”?

Background. Let $\mathcal{C}$ be a symmetric monoidal category with unit $\mathbf{1}$. A subobject of $\mathbf{1}$ is just a monomorphism $I \to \mathbf{1}$. We may also call this an ideal of ...
11
votes
0answers
167 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 ...
11
votes
0answers
157 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 ...
10
votes
0answers
599 views

What is the history of “only if” in mathematics?

A quick search on the use of "only if" returns questions asking about its use and meaning in mathematics, such as here, here and here, revealing confusion in its interpretation and use for some ...
9
votes
0answers
80 views

The term “elliptic”

There are many things which are called “elliptic” in various branches of mathematics: Elliptic curves Elliptic functions Elliptic geometry Elliptic hyperboloid Elliptic integral Elliptic modulus ...
9
votes
0answers
117 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 ...
8
votes
0answers
118 views

What can the reals of an inner model be?

This is probably a silly question. Call a set of reals $X$ a constructibility ideal (in analogy with a Turing ideal) if $X$ is closed under effective join $r\oplus s: n\mapsto 2^{r(n)}3^{s(n)}$ and ...
7
votes
0answers
135 views

Is there a term for a function where equal output values must come from only one contiguous range of input values?

I'm looking for a word to describe a function where every output is guaranteed to have come from exactly one contiguous range of input values. For example, a monotonic function has this property, but ...
7
votes
0answers
162 views

Where does the term “mouse” (in set theory) come from?

Does the term mouse stand for "Model Of Universe with Sequences of Extenders" or perhaps mice stands for "Model Including Cardinal Extensions"? A quick review: Gödel's L-universe is a core model ...
7
votes
0answers
117 views

Why is the sheaf $\mathcal{O}_X(n)$ called the “twisting sheaf” (where $X=\operatorname{Proj}(S)$ for a graded ring $S$)?

Basically my question is why the sheaf $\mathcal{O}_X(n)$ is called the twisting sheaf, here $X=\operatorname{Proj}(S)$ and $S$ any graded ring.
7
votes
0answers
87 views

Is “slightly deform” a well defined concept in mathematical proof?

In topological proofs the phrase "slightly deform" is widely used. To me, although I can accept the idea intuitively, the phrase "slightly deform" does not sound like a strict mathematical concept. ...
7
votes
0answers
154 views

Name of a certain set

I want to know if there is any already-standard way to refer to the sets described as follows. For a set $X$, let $-X = \{-x: x \in X \}$; call it the negative of $X$. Take the set of all primes in ...
7
votes
0answers
141 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 ...
7
votes
0answers
162 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
votes
0answers
168 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
votes
0answers
473 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
6
votes
0answers
237 views

Why “cylinder sets”?

If $I$ is any set of indexes, we define $E^I=\{(x_i)_{i\in I}:x_i\in E\,\,\forall i\in I\}$, $E$ being any set. Subsets of $E^I$ of the form $C_J=\{x_i\in B_i\,\,\forall i\in J\}$, where ...
6
votes
0answers
133 views

Have these (extremely simple) classes of algebraic structures been considered in the literature? If so, what are they called?

Questions. Have the following kinds algebraic structures been considered in the abstract algebra literature etc.? If so, what are they really called? (I have used made-up terminology for the sake ...
6
votes
0answers
249 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 ...
5
votes
0answers
37 views

Does a plane curve with polar equation $r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$ have a name?

Does a plane curve with polar equation $$r=\lambda_1\cos^2\theta+\lambda_2\sin^2\theta$$ where both $\lambda_i>0$ have a name? It's very similar to hippopede, also known as lemniscate of Booth, ...
5
votes
0answers
102 views

Notation/terminology for “independent” subspaces/subalgebras

Let $V$ denote a vector space (or any other kind of algebraic structure). Question. Letting $I$ denote a fixed set and $X$ denote an $I$-indexed family of subspaces (subalgebras) of $V$, is there ...
5
votes
0answers
55 views

a new(?) operation using products of multiplicities

Does the operation $$n \odot m := \prod_{p \text{ prime}} p^{v_p(n) \cdot v_p(m)}$$ on positive integers have a common name? Has this operation been studied somewhere? Notice that $\odot$ is ...
5
votes
0answers
62 views

Definiton of No Tear and No Paste

Topologists often mention an example beginning by "If there is no tear and no paste, then ...". As a student, I am confused with this "term", and I want to know the exact mean of it. First of all, ...
5
votes
0answers
106 views

Can we consider a hypergeometric function as a closed-form?

Let's say a calculus problem like an integral or a series has a solution that inevitably involving a hypergeometric function. It turns out that hypergeometric function cannot be expressed in term of ...
5
votes
0answers
59 views

Why are centers, centralizers and normalizers called that way?

I know what they are, but where do the names come from?
5
votes
0answers
114 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: ...
5
votes
0answers
201 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
votes
0answers
114 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
65 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 ...
5
votes
0answers
52 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
143 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
96 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
525 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
81 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 ...
5
votes
0answers
219 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 ...
4
votes
0answers
55 views

Are the terms 'clan' and 'tribe' common in mathematics?

In the book 'Vector Measures' by Dinculeanu, he starts the discussion by talking about "classes of sets", and introduces two pieces of terminology I've never seen before, and can't find any evidence ...
4
votes
0answers
32 views

What do you call two groups with only trivial homomorphisms between them?

Suppose $G$ and $H$ are groups, and all group homomorphisms $G \to H$ and $H \to G$ are trivial. Is there a common term to describe such a pair of groups with? Like, “$G$ and $H$ are [...]”, or “$G$ ...
4
votes
0answers
39 views

Is there a name for this graph-theoretic concept?

Let $G$ and $H$ be graphs with vertex sets $V$ and $W$, and $f\colon V \to W$ a function. We say that $f$ preserves $k$-neighborhoods if all points that are at distance $k$ from each other in $G$ are ...
4
votes
0answers
116 views

Why is recursion theory suffering from terminological bloat?

Several questions on MSE in recent months and most recently this one have made me feel that recursion theory is suffering from terminology bloat. Why have so many synonyms for "recursive" and ...
4
votes
0answers
45 views

A name for elements of a group generating the same cyclic subgroup

Elements with similar properties usually deserve a name in many contexts, say primitive elements in finite fields, integers modulo a number $n$, generators of a free groups etc. Does there exist a ...
4
votes
0answers
44 views

In mathematics what does it mean “to occur naturally”?

In mathematics, I often meet the expression " 'x' occurs naturally", or " 'x' occurs naturally in 'Y' ". For example: "You should know why eigenvectors and eigenvalues occur naturally in linear ...
4
votes
0answers
110 views

What do we call collections of subsets of a monoid that satisfy these axioms?

Consider a monoid $M$ and a semiring $S$. Then there's an $S$-algebra freely generated by the monoid $M$, which can be described explicitly as the set of all finitely supported functions $M ...
4
votes
0answers
27 views

terminology for a “forward flow” type of random digraph

I am trying to find a characterization of the probability that vertex $1$ is connected to an arbitrary large vertex $N$ in a random digraph. The difference from typical random digraphs is that if ...
4
votes
0answers
50 views

Terminology in graph theory

Let $G$ be a finite graph with the following property: For any vertex $a$ and edge $\{b, c\}$ of $G$, there is an edge connecting them: there is one of $\{a,b\}$ or $\{a, c\}$ in $G$. Is there ...
4
votes
0answers
160 views

When do the zero divisors of a commutative ring form an ideal?

Let $J$ denote the set of zero-divisors of a commutative ring $R$. Since we automatically have $RJ \subseteq J$, hence $J$ is automatically halfway to being an ideal. Furthermore, its already ...
4
votes
0answers
137 views

Terminology: order vs. degree (in general)

The word degree comes from Latin degradus (through French), which means something like step down. The word order comes from Latin ...
4
votes
0answers
102 views

In the mean value theorem, we are guaranteed $c$ such that $f'(c) = (f(b)-f(a))/(b-a)$. Does $c$ have a name?

The Mean Value Theorem says approximately that for differentiable $f$, there is a $c \in (a,b)$ such that $$ f'(c) = \frac{f(b)-f(a)}{b - a}. $$ I presume that the number $f'(c)$ is the mean value. My ...
4
votes
0answers
176 views

Reading mathematical formulas in Russian & German

The book Russian for Mathematicians by Glazunova has a very useful section with examples of how formulas are read in Russian. (Most mathematical dictionaries don't seem to have this, as I suppose they ...
4
votes
0answers
105 views

Have any authors suggested mathematics-wide prefixes for “missing a quotient” and/or “missing an identity”?

The prefixes in the following terms both mean: "missing the obvious quotient by the obvious equivalence relation." seminorm pseudometric Similarly, the prefixes in the following terms both mean: ...