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3
votes
1answer
228 views

Decomposition vs filtration vs stratification

Are there accepted/standard definitions of "decomposition", "filtration", and "stratification" of a topological space (or of a manifold, or of an algebraic variety) $X$? I tend to understand ...
5
votes
3answers
253 views

Does this property of a first-order structure imply categoricity?

Let $\mathfrak{A}$ be a first-order structure over a relational language and let $\kappa$ be an infinite cardinal. Lets say that $\mathfrak{A}$ has the $\kappa$-property if for every structure ...
5
votes
0answers
96 views

Star shaped sets with a midpoint

Suppose $U$ is an open subset of $\mathbb{R}^n$ which is star shaped with respect to $p\in U$. I'll call $p$ a midpoint of $U$ if for any line $\ell$ through $p$, the point $p$ is the midpoint of the ...
0
votes
0answers
106 views

Name of Property $t=st \text{ and } s=ts$

What is the name of the property shared by a pair of functions $s,t$ with $$t=st \text{ and } s=ts$$ ( Main example: relation-valued domain and range operations on relations, via ...
33
votes
5answers
3k views

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

I think we all occasionally come across terminology that we'd like to see supplanted (e.g. by something more systematic). What I'd like to know is, under what circumstances is it reasonable to believe ...
2
votes
0answers
48 views

A category of partially-ordered commutative semirings; name/notation?

Organize $\mathbb{N} \cup \{-\infty\}$ as a semiring $S$ in the max-plus fashion. So in particular, we have $1_S = 0$ and $0_S = -\infty$. Then for every commutative semiring $R$, we get a degree ...
3
votes
3answers
366 views

“countable” topology

Given universal set $U$. Is there any name of the collection of subsets of $U$ (call them quasi-open) satisfying the following axioms: i) $\emptyset$ and $U$ are quasi-open; ii) finite intersections ...
33
votes
2answers
4k views

How did “normal” come to mean “perpendicular”?

How and when did the word "normal" acquire this meaning? When I first thought of this, I couldn't really come up with any explanation that wasn't complete speculation -- pretty much all I was able to ...
9
votes
2answers
423 views

Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...
2
votes
2answers
178 views

What do we call functions that behave like predicate symbols?

Assume a metatheory that supports lambda-abstraction, and an object language that is merely first-order. Now let $\varphi$ denote a formula in the object language with one free variable $x$. Then we ...
3
votes
1answer
160 views

Coxeter groups - Parabolic subgroups

In the theory of Coxeter groups there is the notion of so called parabolic subgroups. I'm wondering is this term just a random name, or there are some historical reasons? Why parabolic? Thanks.
4
votes
1answer
200 views

What is an element of an iterated tangent bundle?

An element of the tangent bundle $T M$ of a manifold is called a "(tangent) vector". An element of its dual $T^* M$ is called a "covector" or a "1-form". An element of the exterior square ...
6
votes
3answers
310 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 connected and $U$ is nonempty? In other words, this ...
5
votes
0answers
233 views

Primes for which 2 is a primitive root

I am writing a paper in which I keep referring to primes p for which 2 is a primitive root mod p and so I want to give a name for these primes. Is there a name for these primes in the literature ...
3
votes
2answers
183 views

Definition of the Moebius Ladder Graph

I found two different definitions of the Moebius Ladder Graph, whose essential difference is, whether the smallest one shall be $K_4$ or $K_{3,3}$. according to Wikipedia ...
3
votes
0answers
125 views

Correspondence between numerical semigroups and polynomials?

A numerical semigroup $A$ is defined as a subsemigroup of the semigroup $(\mathbb{N},+)$ of the positive integers such that the set $\mathbb{N}\setminus A$ is finite. Equivalently (for a subsemigroup) ...
2
votes
1answer
123 views

Terminology for the equation $a=a+b$ in commutative semigroups

Let $(S,+)$ be a commutative semigroup. For $a,b\in S$ consider the equation $a=a+b$. Does such a relation between the given $a$ and $b$ have a name? I am currently using such equations quite often ...
12
votes
1answer
703 views

Why the name “variety” and the notation “V” for zeroes of polynomials?

The following questions came to my mind while preparing the notes for the first class of (my first) course on algebraic geometry. Question 1: Is there any motivation for choosing the term "variety" ...
3
votes
1answer
224 views

Colorful model theory

There are a number of concepts in model theory - often situated around Hrushovski's amalgamation method (see for instance http://math.univ-lyon1.fr/~wagner/nijmegen.pdf) - which are colorfully named: ...
10
votes
1answer
628 views

Why are they called Specht Modules?

I know that the simple modules of $\mathbb{C}S_n$ are called Specht Modules, and they are named after the German Mathematician Wilhelm Specht because he studied them, but I think these modules were ...
3
votes
1answer
354 views

What is the correct preposition? (And is there one?)

I just stumbled upon a linguistic problem I wasn't able to resolve via web search. Suppose we're given some geometric set $A$ and subset $B\subset A$. Isn't there a compact way of saying that there ...
2
votes
0answers
70 views

Terminology for real closure relative to a normal number field?

A real subfield $R\subseteq F$ of any number field has (finitely many) maximal real intermediate fields $R\subseteq R'\subseteq F$. Can I call such an $R'$ a real closure of $R$ relative to $F$? ...
2
votes
0answers
144 views

Why is a spectrum (in topology) called a spectrum? [duplicate]

The title says it all, I guess. Thank you for your answers.
8
votes
0answers
167 views

Earliest use of the term “linearly reductive”?

Recently a number of MO questions have referred to a "linearly reductive group", usually in a way that is out of focus. It's unclear to me why this terminology is so popular, since over a field of ...
28
votes
3answers
1k views

Why aren't fields called “bodies” instead?

The discrepancy regarding the names of commutative division algebras in German and English has always startled me. In English they are called fields, whereas their original German name is Körper ...
7
votes
2answers
273 views

Why the term “monad” in homological algebra?

Which is the origin and the reason for the choice of the term "monad" in the sense of homological algebra? Does this concept have any relation whatsoever to the "monads" from category theory?
6
votes
1answer
391 views

Origin of the term “weight” in representation theory

In representation theory, there are the related concepts of weights and roots. Since both are kinds of generalised eigenvalues, and eigenvalues are roots of e.g. the characteristic polynomial, the ...
1
vote
0answers
143 views

Terminology question in model category theory

This is a terminology question. That will help me to write down my papers. In Marc Olschok's PhD available here (I cannot find it anymore on the Internet so it is in my webpage, the original URL is ...
4
votes
0answers
140 views

Nesting big-O with big-Omega $O(g(\Omega(h(n))))$: is it $O$ for all $\Omega$ or for one $\Omega$?

I want to express the following statement about a function $f(n)$: there exists $f_\Omega\in\Omega(h(n))$ such that $f\in O(g(f_\Omega(n))$. What's the correct notation for this? Is it $f\in ...
3
votes
3answers
191 views

Slice-category-like terminology question

Let $\mathcal C$ be a category, and consider a new category $\mathcal C'$ with $Obj(\mathcal C') := \{$pairs $(X \in Obj(\mathcal C), T \in End_{\mathcal C}(X)) \}$ $Hom_{\mathcal ...
4
votes
2answers
237 views

Is there a name for relations with this property, and the category of them?

The following math.stackexchange question asked whether there is a name for a certain sort of relation. I have become interested in the question, and no one suggested a name there, so I am asking ...
1
vote
1answer
97 views

Inverses of two-argument functions with respect to one argument

I asked a shorter version of this question at math.stackexchange.com four days ago but it hasn't gotten any answers or comments. Consider a function $f : A \times B \to C$ and two inverses, each with ...
3
votes
1answer
281 views

Is “ultracompact” taken?

Almost-huge cardinals are characterizable in terms of coherent towers of supercompactness measures, with a certain property of the direct limit model (see Kanamori's book). A useful large cardinal ...
0
votes
1answer
161 views

Terminology for a Partition of a Set which Includes Empty Sets

Mostly I see a partition of a set A defined as a collection of non-empty disjoint sets whose union is A. I see one reference that allows empty sets to be included in the partition: ("Potter, M. "Set ...
2
votes
0answers
181 views

“Extended” Weil Cohomology Theories

According to Wikipedia, a Weil cohomology theory is a functor from the category of smooth projective varieties over a field $k$, to graded algebras over a field $K$ of characteristic zero, together ...
1
vote
0answers
159 views

What is this structure called?

(I'm not entirely sure what to tag this; feel free to retag.) While thinking about automata (specifics below), I ran into the following phenomenon: A cofunction system is a pair of sets $X, A$, ...
3
votes
2answers
330 views

Terminology for blowups in algebraic geometry

This is a partial duplicate of this Stack Exchange question which unfortunately got no answer. All schemes are Noetherian and of finite type, although they need not be normal. With $Z \subset X$ a ...
6
votes
0answers
89 views

How to call a point in a space having the property that there is essentially one $\omega$-sequence converging to it?

Consider the point $x=\langle \omega_1,\omega\rangle$ in the Tychonov plank $(\omega_1 + 1)\times(\omega + 1)$. Then there is essentially only one sequence (of length $\omega$) converging to it, ...
2
votes
0answers
109 views

A generalization of quasi-identities

In universal algebra, a variety is axiomatized by identities $t \approx s$ between terms $t$ and $s$. More general are quasi-varieties that are axiomatized by quasi-identities of the form $$u_1 ...
4
votes
1answer
356 views

Where does the name “Reynolds operator” come from?

I always found it strange that, in the context of invariant and representation theory, averaging over the group is called the "Reynolds operator". As far as I know the work of Reynolds was in fluid ...
3
votes
1answer
155 views

Pairs of paths with the same source and target

Commutative diagrams usually express path equivalences in a category and thus involve pairs of paths in a category with the same source and target. General diagrams - in categories resp. category ...
0
votes
1answer
58 views

Name for a Specific Type of Non-Symmetric Bilinear Form

Let $V$ be a finite dimensional vector space, with some choice of basis $\{e_i\}_{i \in I}$. With respect to an idempotent bijection $B:I \to I$, define a bilinear form by $$ g = \sum_{i=1}^N ...
6
votes
1answer
229 views

Why stationary sets were named such?

My question is about terminology: Do you know why stationary sets were named such? Going over the following MO question about the intuition behind stationary sets, the only compelling argument I can ...
10
votes
2answers
533 views

What are Moschovakis cardinals?

The question is exactly that of the title: what are Moschovakis cardinals? Background. In a recent answer to the question, "Are there examples of statements that have been proven whose consistency ...
6
votes
1answer
201 views

Terminology question for poset maps

Is there a standard name for order-preserving maps $f\colon P\to Q$ of posets with the property that the image of a lower set is a lower set, or equivalently if $q\leq f(p)$ then there exists $p'\leq ...
3
votes
0answers
117 views

term for a rectangle with a bounded aspect ratio

I am writing a peper about dividing a shape into rectangles, where the main issue is to make sure that the rectangles have a limited aspect ratio. I am looking for a clear, unambiguous term for such ...
3
votes
0answers
163 views

choosing between the two ways to tropicalize

When tropicalizing a subtraction-free expression (see Do all subtraction-free identities tropicalize?), is it more common to replace addition by max or by min? Related issues: Is there a name for ...
2
votes
1answer
99 views

Hilbert's Finiteness Theorem for connected semisimple Lie groups in Weyl's “Classical Groups”

First of all, sorry for using this account. Somehow I can't login to my previous one anymore and am thus using the account associated to my MSE one. Also, I already asked the question on MSE, but ...
2
votes
2answers
59 views

Hilbert's Finiteness Theorem for connected semisimple Lie groups over $\mathbb{C}$ in Weyl's “Classical Groups” [duplicate]

In Nagata's "Lectures on the 14th problem of Hilbert" I found a reference to Weyl's "Classical Groups". Nagata writes that Weyl gives a positive answer to the original problem If ...
1
vote
0answers
72 views

Terminology question: maximal non-branching directed paths

Is there any special word for a maximal non-branching directed path in a network or diforest? To be 100% precise, by "maximal non-branching directed path" I mean a path $P=x_1,x_2,\ldots$ (maybe ...