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    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeSep 28th 2013
    • (edited Sep 28th 2013)

    There was already a discussion of ends in the topological sense at proper homotopy. (I had never seen the term hemicompact before. I knew of σ\sigma-compact which is almost the same.)

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeSep 28th 2013

    Yes, I wrote end compactification based off of Wikipedia. I still want to convince myself that this is all self-consistent.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 28th 2013

    At proper homotopy theory, the definition uses the closures of compact subspaces rather than the compact subspaces themselves. It does seem to be a little easier to define the concept using these. Are there examples to show why one way is better than the other? Or are they secretly equivalent?

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeSep 28th 2013

    I quote from Wikipedia

    Every hemicompact space is σ-compact. The converse, however, is not true; for example, the space of rationals, with the usual topology, is σ-compact but not hemicompact.

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeSep 29th 2013

    Yes, I noticed that. I don't know if that was in answer to my question

    Are there examples to show why one way is better than the other? Or are they secretly equivalent?

    but that's not what I was asking about.

    I was asking about using compact subpsaces versus the closures of compact subspaces in the definition of ‘end’.