> Within the definition presented there is a limit definition for sets > that is derived from the underlying topology on the elements of > those sets. At such it appears to me to be a natural definition, > that is, an element is also element of the lim sup, it should be a > limit point of one of the many pointwise sequences you can create > when you take from each of the sets an element. lim inf consists of > those elements that are limits of such pointwise sequences.
So, it's a kind of "lifting" of the definition of limit to sequences of subsets of a topological space. Yes, that's fairly natural, though it's still a different notion than a limit.
-- Jesse F. Hughes "Mathematicians who read proofs of my results seem to basically lose some part of themselves, like it rips at their souls, and they are no longer quite right in the head." -- James S. Harris, Geek Cthulhu