2
$\begingroup$

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 $A \subseteq B$ ?

  • 1
    In the Context of partition it is clear what it means.2011-12-17
  • 3
    "Refinement" usually has [this meaning](http://en.wikipedia.org/wiki/Refinement_(topology)#Refinement) in topology.2011-12-17
  • 5
    Perhaps adding a little more context (and maybe even the name of the book, chapter and perhaps also page number) could help.2011-12-17
  • 1
    "Any partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that ρ is coarser than α—if every element of α is a subset of some element of ρ. Informally, this means that α is a further fragmentation of ρ. In that case, it is written that α ≤ ρ." From: http://en.wikipedia.org/wiki/Partition_of_a_set2011-12-17
  • 0
    @gnometorule: Refinement is a word which has contexts. In the context of partition you are correct, however it can be applied to a different context (topologies, for example).2011-12-17
  • 0
    Agreed. But see his tag: elementary set-theory.2011-12-17
  • 1
    @gnometorule: That is my tag. The original was both [set-theory] and [elementary-set-theory]. The two tags may coexist if there is a damn good reason. Until the OP returns with a reason (i.e. a reference) I would rather assume that it is an elementary problem. Moreover one can consider the possibility of refinement of topoligies as elementary just as well.2011-12-17

1 Answers 1