Editing Associated bundle (section)

==An example==

A simple case comes with the [[Möbius strip]], for which <math>G</math> is the [[cyclic group]] of order 2, <math>\mathbb{Z}_2</math>. We can take <math>F</math> to be any of the following: the real number line <math>\mathbb{R}</math>, the interval <math>[-1,\ 1]</math>, the real number line less the point 0, or the two-point set <math>\{-1,\ 1\}</math>. The action of <math>G</math> on these (the non-identity element acting as <math>x\ \rightarrow\ -x</math> in each case) is comparable, in an intuitive sense. We could say that more formally in terms of gluing two rectangles <math>[-1,\ 1] \times I</math> and <math>[-1,\ 1] \times J</math> together: what we really need is the data to identify <math>[-1,\ 1]</math> to itself directly ''at one end'', and with the twist over ''at the other end''. This data can be written down as a patching function, with values in <math>G</math>. The '''associated bundle''' construction is just the observation that this data does just as well for <math>\{-1,\ 1\}</math> as for <math>[-1,\ 1]</math>.