Re: Set theory: what is meant by "unbounded"?

On Jun 25, 3:35 pm, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Sun, 24 Jun 2007 13:41:33 -0700, Snis Pilbor <snispil...@xxxxxxxxx>
wrote:

In his "Set Theory", Kunen says that a map f:a->b maps a "cofinally"
into b if range(f) is "unbounded" in b. What on earth does he mean by
"unbounded" here?

Same as what "unbounded" always means: There does not exist
y in b such that f(x) <= y for all x in a.

Presumably a and b are sets on which there exists a natural
partial order, or one has been assumed?

(Also: It doesn't seem to me that unbounded is the same
as cofinal unless f is _nondecreasing_, in the sense
that s <= t implies f(s) <= f(t). Is that the case here?)

The word is not in his index (nor is "bounded") and I can't find it anywhere.

************************

David C. Ullrich

They are most probably sets of cardinals with the usual ordering. I
think f need not be 'nondecreasing'.

Regards

.

Relevant Pages