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    • 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 XX was not required to be locally compact. So if XX is the space of rational numbers (as a subspace of the real line), then a function like xe x 2x \mapsto \mathrm{e}^{-x^2} (taking values in the real line with basepoint 00) should vanish at infinity, but there are too few compact subspaces of XX 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.

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