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Property Suggestion: Finite dimensional CW complex #1768
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Would be nice to include the following space since I think it's one of the basic examples of a finite dimensional CW complex, and sort of fits in with the klein bottle, torus, and projective plane since its obtained by gluing the boundary of a single disk: https://en.wikipedia.org/wiki/Dunce_hat_(topology)
It satisfies: Finite dimensional CW Complex + ~Locally Euclidean space with boundary + Contractible + ~Has a cut point
Except for the ~Has a cut point part, that's also satisfied by spaces obtained by gluing a finite number of closed or half open intervals at the left endpoints.
Reacted by Felix Pernegger
We dont have to do this now (first lets deal with CW complex and weakly contractible etc), but this is a very common variant of a CW complex. I dont think we can encode it currently (unlike Finite CW complex).
A CW complex is finite dimensional iff the skeleta stabilise. Notably its nontrivial to prove this is preserved by homeomorphisms/well-defined.a