What does "refinement" mean?
I was reading a book and it had the following sentence:
$A$ is a refinement of $B$
where $A$ and $B$ are sets.
What does this mean? Perhaps $A \subseteq B$ ?
Solution 1:
Here are the two notions of refinement that come up most often in my work:
A topology $\tau$ on a set $X$ refines another topology $\sigma$ on $X$ if $\sigma\subseteq\tau$.
If $P$ and $Q$ are partitions (or covers) of a set $X$, then $P$ refines $Q$ if for all $U\in P$ there is $V\in Q$ such that $U\subseteq V$.