I was trying to understand the notion of CW complex from wikipedia. The very first non-example is:
$$\{re^{2\pi i \theta} : 0 \leq r \leq 1, \theta \in \mathbb Q\} \subset \mathbb R^2$$
This is not a CW complex, supposedly because it is not locally contractible.
Could someone help me with why a CW complex(as defined in the wikipedia page) has to be locally contractible?
