David Macmanus wrote:

"Edward Green" wrote in message
ups.com


(I) A metric space is closed if it contains all its limit points;
elements X s.t. for all eps there exists an element Y s.t.|X-Y| eps

Thanks.
What do s.t. and eps stand for?
Thanks.

"such that" and "epsilon"

You are welcome. However, I think you may probably safely ignore my
response and prefer michaeld's. I was about to add the following tag
to his post:

"Oops! That's what comes from trying to reason from the definitions
and not knowing the culture of the thing".

The idea that "closed" doesn't make much sense applied to a space would
tie in with the tacit assumption of the existence of the limit point,
independent of its existence in the target set, whereas in the
definition of "complete" it is said that the given sequence "converges"
implying both the existence and inclusion of the limit in the
set/space. The idea that the limit could exist but outside the target
set doesn't come up.

Thanks for posting a substantive question.