Tagged Questions

7
votes
1answer
82 views

Is there a name for relations with this property?

Is there a name for relations $\rho : X \rightarrow Y$ such that for all $x,x' \in X$ and all $y,y' \in Y$ we have that the following conditions $$xy \in \rho$$ $$x'y \in \rho$$ $$xy' \in \rho$$ imply ...
1
vote
1answer
33 views

Definition of correspondence

A one-to-one correspondence is an alternative name for a bijection between two sets, but to what does the term 'correspondence' alone refer? As far as I can see, it seems to be another term for ...
2
votes
2answers
36 views

Name of the order with irreflexivity, antisymmetry and transitivity?

I have an order otherwise poset aka partial order but it is irreflexive so relationships such as 1R1 and 2R2 are impossible. What is the name of this order?
3
votes
1answer
76 views

Mono's and Epi's in the category Rel?

Sorry to ask such a trivial question, but I can't find the answer anywhere. Question. What are the monomorphisms/epimorphisms in Rel? Furthermore, what's the standard terminology for describing ...
3
votes
2answers
78 views

If $\sim$ is an equivalence relation on $X$, and there is a strict total order on $X/\sim$, what kind of ordering does $X$ have?

I would like to know if there's a special name for this kind of ordering. When I say there is a strict total order on $X/\sim$, what I mean is that two distinct elements in the same equivalence ...
2
votes
3answers
185 views

Why is 'Antisymmetry' named so?

So when we talk about order relations for the familiar number systems, we are always introduced to the antisymmetry property which is $x \le y, x \ge y \implies x=y$. When I think of the word ...
11
votes
2answers
301 views

When does “pairwise” strengthen and when does it weaken?

"Pairwise disjoint" is stronger than "disjoint"; it sometimes happens that $\displaystyle\bigcap\limits_{i\in I} A_i=\varnothing$ but for every $i,j$, or at least for some, one has $A_i \cap ...
1
vote
1answer
234 views

Empty set as a relation

The empty set is an $n$-ary relation for every $n$, right? How should we call a pair $(n;r)$ consisting of some number $n$ and an $n$-ary relation $r$? To specify $n$ is necessary only when $r$ is ...
1
vote
1answer
116 views

Name of binary relation: if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$

Is there a term for a binary relation $R\subset A^2$ on some set $A$ such that if $(x, y)\in R$ then there is no $z$ such that $(y, z)\in R$ ? Are there any examples of it? Are there any related ...
0
votes
1answer
39 views

Two terminology question about relations

Is there a name for constructing a set from a relation (or, more generally speaking, from a set of pairs that are tuples)? For example, let $R = \{(0, 1), (1, 2), (2, 3)\}$; if you collect all the ...
3
votes
3answers
147 views

What's the name for the equivalence induced by a function on its domain?

Any function $f$ with domain $X$ induces an equivalence relation on $X$, with classes $$\{f^{-1}(\{y\})\,:\, y \in \operatorname{im}f\;\} .$$ Is there a name for this equivalence? Thanks!
1
vote
0answers
50 views

Term for generalized antisymmetry?

As I understand it, a binary relation $R$ over a set $A$ is antisymmetric if for all $a, b \in A: aRb \land bRa$ implies $a = b$. Now, suppose that I have an equivalence relation $E$ over the set ...
2
votes
1answer
133 views

Is there a name for this type of binary relation?

Suppose that $X$ is a set and $\sim$ is a binary relation on $X$ that satisfies for all $x,y \in X$; if $x \sim y$ then $x \sim x$ and $y \sim y$. Is there a name for this type of relation? I am ...