I don't understand the fibre bundle structure of the Mobius band, described by my textbook.(adsbygoogle = window.adsbygoogle || []).push({});

"The base space ##X## is a circle obtained from a line segment L as indicated in Fig. by identifying its ends. The fibre ##Y## is a line segment. The bundle ##B## is obtained from the product ##L \times Y## by matching the two ends with a twist.

[The projection ##L \times Y \rightarrow L## carries over under this matching into a projection ##p: B \rightarrow X##. Any curve as indicated with end points that match provides a cross-section. Any two cross-sections must agree on at least one point. There is no natural unique homeomorphism of ##Y_x## with ##Y##. There are two such which differ by the map ##g## of ##Y## on itself obtained by reflecting in its midpoint. The group ##G## is the cyclic group of order 2 generated by ##g##.]"

What I don't understand are in brackets.

Could someone help me to clarify more clearly?

Regards.

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# The Mobius band

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