Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Both answers to this question seem equally reasonable to me.

If the answer is positive, I have no idea what the construction of such a space would look like....

If the answer is negative, I assume one would try to subdivide the cells somehow... but I don't really know how that would go.

I guess this came up because I was trying to think of an example of a CW-complex that wasn't homeomorphic to a Delta-complex... and figured the easiest way to make such a thing would be to make one that is not homotopic. This, of course, doesn't seem much easier to build, but at least easier to prove once you're done building.

share|cite|improve this question
By "homotopic" you mean "homotopy-equivalent" yes? CW complexes all have the homotopy type of simplicial complexes, so also of delta complexes. You can make the argument inductively -- argue that if you attach a cell to a simplicial complex, you get something with the homotopy-type of a simplicial complex. Have you read (for example) the proof of excision for singular homology? –  Ryan Budney Dec 4 '10 at 0:22
Ah, of course! Yes, I have. I should've given this more thought before asking :) –  Dylan Wilson Dec 4 '10 at 0:25

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.