2
$\begingroup$

I'm reading "Memento on cell complexes" and the following is supposed to be a counter example of a cell complex because $e^1$ is not homeomorphic to the open segment:

enter image description here

To me this looks like a deformed disk and is therefore homeomorphic to $D^2$. Why is $e^1$ not homeomorphic to the open segment? Or is it missing a second black dot to denote touching of $e^1$ at 12 o'clock?

Also, I don't see why the following isn't a cell complex either. The boundary of $e^2$ maps into $X^1$. The inductive construction of a cell complex requires exactly that.

enter image description here

Thanks for your help!

  • 1
    @RyanBudney and t.b. , is there a reason you left comments only and not answers? It looks like this question is resolved but I can't tell for sure because it hasn't been officially marked as such.2012-10-05

0 Answers 0