TITLE: What is the one-point compactification of the Loch Ness Monster?
QUESTION [7 upvotes]: The Loch Ness Monster surface is the noncompact orientable surface with one end accumulated by genus. If we take the one-point compactification of this surface we get some surface with finite genus by the classification. and get a manifold, it would have finite genus by the classification. This seems a little absurd.
What is the one-point compactification of the Loch Ness Monster, and in general, is there any intuition behind determining compactifications of surfaces with infinite genus?

REPLY [2 votes]: This space (the one-point compactification) is not homeomorphic to any of the "standard" spaces you encounter in your topology classes (in particular, it is not a surface). Just call it "the one-point compactification of the Loch Ness Monster" (OPCOLNM), if you are looking for a nice name. As for the intuition of such spaces, I do not know what to say, there is none as far as I know. You may want to read some papers on the classification of noncompact surfaces, which uses compactifications to classify these. See my answer here for a reference and some discussion where I describe the "end compactification" in concrete terms.
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