Let's take a simple example.(adsbygoogle = window.adsbygoogle || []).push({});

Both a cylinder and Möbius strip consist of a circle with a line segment associated with each point of the circle. The cylinder is considered truly equivalent to the direct product S1 X line segment while the Möbius strip is only locally like S1 X line segment. Ok, what does that mean? Does the direct product have any properties whicharen'tlocal?

I mean, I thought S1 X line segment L is merely [tex]\{(p,x)|p \in S^1, x \in L\}[/tex], period. Both the cylinder and Möbius strip would be instances of this general thing, differing from each other only in additional properties, e.g. the transition functions.

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# How does a fibre bundle differ from base space X typical fibre?

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