Local and Global Sections
Fiber bundles do not in general have such global sections, so it is also useful to define sections only locally. A local section of a fiber bundle is a continuous map s : U → E where U is an open set in B and π(s(x)) = x for all x in U. If (U, φ) is a local trivialization of E, where φ is a homeomorphism from π−1(U) to U × F (where F is the fiber), then local sections always exist over U in bijective correspondence with continuous maps from U to F. The (local) sections form a sheaf over B called the sheaf of sections of E.
The space of continuous sections of a fiber bundle E over U is sometimes denoted C(U,E), while the space of global sections of E is often denoted Γ(E) or Γ(B,E).
Read more about this topic: Section (fiber Bundle)
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