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Example 1.
Define some manifolds.
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Define transformations F: M -> N; G: P -> M; H: N -> Q.
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Compute the compositions F o G, H o F and H o F o G.
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Example 2.
We can express the transformation T: P -> P as the composition of 3 transformations A, B, C.
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Example 3.
We can check that the transformation K is the inverse of the transformation F.
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Example 4.
If pi: E -> M is a fiber bundle, then a section s of E is a transformation s: M -> E such that pi o s = identity on M.
Check that the map s is a section for E.
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