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Is there a difference between "ideal boundary" as in Kerekjarto's theorem and "ends" as in the usual topological sense? All I can see is that the former is applicable to bordered surfaces as well as open ones, whereas the latter is only applicable to open, non-compact surfaces. Though I may be very wrong...

Thanks.

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    Which theorem of Kerékjártó? I think he may have proven more than just one theorem in his life. It'd be great if you can either summarise the theorem or give a link to a standard reference on it.2011-08-20

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If you mean Kerekjarto's Classification Theorem for non-compact surfaces, then essentially the definitions are the same, at least according to the statement and definition of ideal points in this review paper. Perhaps one may say that Kerekjarto defined his notion only for surfaces, but that's a minor point.

If your definition of "ideal boundary" differs from that of the linked paper (p11), please edit the question and supply it.

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    @Brian: you should probably ask that as a new question. This time make sure to include all the relevant definitions and try to make the question as self-contained as possible. Cheers.2011-08-22