Re: Extended real line question

On 28-05-2007 21:22, mathman wrote:

Consider the extended real line [-\infty;+\infty] (where "\infty" is the term used to denote "infinity"). It can be naturally equipped with the order topology.

I would like to know how to show that this extended real line is the closure of the (classical) real line.
Every neighborhood of +oo contains some interval of
the form
(x,+oo] and therefore it contains real numbers. So
+oo belongs
to the closure of real line.

The real line without oo or -oo is a closed set,

*Every* topological space is a closed subset of itself.

so those "numbers" aren't in the closure under ordinary
topology (generated from open intervals).

No? Then where is the fault in my proof?

Best regards,

Jose Carlos Santos
.