Transition function

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In mathematics, a transition function has several different meanings:

  • In topology, a transition function is a homeomorphism from one coordinate chart to another. Given two charts (Ui, φi) and (Uj, φj) a transition function normally takes the form
\phi_i\phi_j^{-1} : (U_i \cap U_j) \times F \to (U_i \cap U_j) \times F
for some set F being covered by the topology. See fiber bundle and atlas (topology) for additional details.
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