# Fiber Bundle: Hairbrush

I am trying to understand the hairbrush example of a fiber bundle from the Wikipedia article on fiber bundles.

If I am understanding this, in the hairbrush example E is the hairbrush, ie. all the bristles with the cylinder they are attached to, B is the cylinder attaching the bristles, F are the bristles, and $\pi$ maps a bristle to the point on the cylinder it is attached to. So is $E$ in this case equal to $B\times F$? Now pick a bristle $x$, and a small neighbourhood $U$ of $\pi(x)$. Then $\pi^{-1}(U)$ are all the bristles attached to the cylinder somewhere in $U$, and does this include $U$ itself?

I think the idea is that the hairbrush looks like a cylinder itself, but I am a bit confused.

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 Since this can be thought of as the normal bundle,