section

A section (informally) is how to look up into a cover or fiber bundle.

Definition

For $\pi :E\to M$ a continuous map, a section of $\pi$, $\sigma :M\to E$ is a continuous right inverse.

i.e. $\pi \circ \sigma ={\text{Id}}_M$ Or written another way, $\sigma :M(\text{or }U\subset M)\to E\text{s.t. }\sigma (p)\in {\pi }^{-1}(\{p\})\forall p\in M(U)$ If $U\subset M$ is used, then it is called a local section of $\pi$.

Types

There can be smooth sections or just continuous ones.

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References

smooth manifold