Let \((B,d),(E,d)\) be metric spaces. A section of \(E\) over the base space \(B\) is a continuous right inverse \(\sigma :B\to E\) of a surjective function \(\pi :E\to B\), i.e. a function \(\sigma\) such that \[\pi (\sigma (x))=x\] for all \(x\in B\).
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