Talk:Cellular approximation theorem
Add topicLatest comment: 9 months ago by Dan Gluck in topic Possible error in relation to compactness
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Referencing Hatcher
[edit]Is saying "for details, see Hatcher" sensible here? - or is the best step just to expand this article into showing more of the proof. ChthonianDepths (talk) 15:41, 17 October 2024 (UTC)
Possible error in relation to compactness
[edit]The article states "Then it is a general result of CW-complexes that any compact subspace of a CW-complex meets (that is, intersects non-trivially) only finitely many cells of the complex. "
I believe the actual known theorem is with "only finitely many OPEN cells of the complex", i.e. interiors of cells. (E.g., take a point with infinite number of higher cells attached to it as a counter example to the original statement). The proof of course still works with the corrected statement. Dan Gluck (talk)\ Dan Gluck (talk) 12:15, 2 October 2025 (UTC)