2
votes
0answers
42 views

Good topologies on $\mathcal{P}(X)$

Let $X$ be a topological space, and let $\mathcal{P}(X)$ (resp. $\mathcal{P}_0(X)$) be the set of all subsets of $X$ (resp. the set of all non empty subsets of $X$). Finally, let ...
1
vote
2answers
93 views

Some equivalence relation from flipping binary trees

I know almost nothing in combinatorics, so this question might be very easy, or well-known. Fix a number $n$. We will consider rooted planar binary trees with $n$ leaves. We will distinguish between ...
5
votes
1answer
275 views

Is this alternative definition of 'equivalence relation' well-known? useful? used?

I discovered that $$R \textrm{ is an equivalence relation on } A \;\equiv\; \langle \forall a,b \in A :: aRb \:\equiv\: \langle \forall x \in A :: aRx \equiv bRx\rangle \rangle$$ The nice thing about ...
3
votes
1answer
123 views

Name of a simple equivalence relation on real numbers?

Define the relation $x \sim y$ where $x$ and $y$ are real numbers to hold if and only if there exist natural numbers $n$ and $m$ such that $x^n = y^m$. It is easy to see that $\sim$ is an equivalence ...
1
vote
1answer
103 views

Functions that are compatible with equivalence relations over its domain and codomain

Given a function $f : X \to Y$, an equivalence relation $\sim_X$ on $X$ and an equivalence relation $\sim_Y$ on $Y$, there is a notion of ``compatibility'' between $f$, $\sim_X$ and $\sim_Y$ if the ...