# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 10th 2013
• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeApr 10th 2013

I added to the statement under Properties; it’s a lot clearer I think to state it first for the one-point compactification.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeApr 15th 2013

The article seemed strangely limited in scope, so I generalised it somewhat. Also an Idea section, which motivates the definition.

• CommentRowNumber4.
• CommentAuthorTobyBartels
• CommentTimeApr 15th 2013
• (edited Apr 15th 2013)

Actually, in some ways it was too general, since originally $X$ was not required to be locally compact. So if $X$ is the space of rational numbers (as a subspace of the real line), then a function like $x \mapsto \mathrm{e}^{-x^2}$ (taking values in the real line with basepoint $0$) should vanish at infinity, but there are too few compact subspaces of $X$ to see this. The article currently doesn't have a definition that includes this, but at least it doesn't exclude this either.

ETA: Actually, the comment about the Stone–Čech compactification seems to cover this, but I'm not sure how generally this can be made to work.