Weak topology on CW complex $X$ is defined with a condition:
Subset $A \subseteq X$ is open in $X$ iff $A \cap e$ is open in $e$ for every cell $e$ in $X$.
As far as I understand, in case when CW complex is embedded in Euclidean space, the induced Euclidean topology and the weak topology do not necassary coincide on infinte CW complexes, but I can't imagine any simple example of such CW complex.
Can anyone give me an example and show why it is better to take the weak topology?
Thanks!