I'm trying to understand better what Hatcher does in the beginning chapter on cell complexes and so in this sense I would really like someone to elucidate for me what are the subcomplexes of $S^{\infty}$, with the cell structure described in the book, having two cells in each dimension.

The clearer the explanation the better! Thanks

  • $\begingroup$ Have you tried making the list of subcomplexes yourself? For example. What are the 1-dimensional subcomplexes? $\endgroup$ – Mariano Suárez-Álvarez Feb 8 '13 at 6:32
  • $\begingroup$ of course i tried; I'm pretty sure the subcomplexes are the $n$-dimensional spheres and the $n$-dimensional spheres, each along with an $n+1$ cell attached to the previous sphere along its boundary. but i was hoping for a detailed answer... $\endgroup$ – TJIF Feb 8 '13 at 6:47
  • $\begingroup$ Why don't you write what you did in the question? $\endgroup$ – Mariano Suárez-Álvarez Feb 8 '13 at 6:50
  • 1
    $\begingroup$ @TJIF - do you understand how to make, for example, $S^2$ with two cells in each dimension (less than 3). $\endgroup$ – Joe Tait Feb 8 '13 at 9:39
  • $\begingroup$ got it, thanks. $\endgroup$ – TJIF Feb 21 '13 at 2:45

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