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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeApr 10th 2013
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   Author: Urs
   Format: MarkdownItex_[[vanishing at infinity]]_

   vanishing at infinity

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeApr 10th 2013
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   Author: Todd_Trimble
   Format: MarkdownItexI added to the statement under Properties; it's a lot clearer I think to state it first for the one-point compactification.

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

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeApr 15th 2013
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   Author: TobyBartels
   Format: MarkdownItexThe article seemed strangely limited in scope, so I generalised it somewhat. Also an Idea section, which motivates the definition.

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

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeApr 15th 2013
   • (edited Apr 15th 2013)
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   Author: TobyBartels
   Format: MarkdownItexActually, 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.

   Actually, in some ways it was too general, since originally was not required to be locally compact. So if is the space of rational numbers (as a subspace of the real line), then a function like (taking values in the real line with basepoint ) should vanish at infinity, but there are too few compact subspaces of 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.