
Re: compact
Posted:
May 16, 2013 10:42 AM


On Wed, 15 May 2013 16:26:54 0500, quasi <quasi@null.set> wrote:
>dullrich wrote: >>William Elliot wrote: >>> A point x is an accumulation point of A >>> when for all open U nhood x, U /\ A is infinite. >>> >>> If S is compact, then every infinite set A has an >>> accumulation point. >>> >>> Proof. >>> If not, then for all x, there's some open U_x nhood x with >>> finite U /\ A. Since C = { U_x  x in S } covers S, there's >>> a finite subcover { U_x1,.. U_xj } >>> Thus A = A /\ (U_x1 \/..\/ U_xj } >>> = (U_x1 /\ A) \/..\/ (U_xj /\ A), >>> is finite, >> >>"has cardinality less than A", not "is finite". > >Looks like a finite union of finite sets, no?
A typo, sort of. Later in the same post he said "is finite", where he should have said "has cardinality less than A". So I decided to post a comment, and then I inserted the comment in the wrong place, this paragraph looking so much like that paragraph...
> >>> which of course it isn't. > >quasi

