Definition:Section (Topology)
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Definition
Let $M, E$ be topological spaces.
Let $\pi: E \to M$ be a continuous surjection.
Let $I_M: M \to M$ be the identity mapping on $M$.
Then a section of $E$ is a continuous mapping $s: M \to E$ such that $\pi \circ s = I_M$.
Also known as
Some authors use the word cross section as opposed to section.
Also see
Sources
- 2003: John M. Lee: Introduction to Smooth Manifolds: $\S 10$: Local and Global Sections of Vector Bundles