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Line 1: In [[mathematics]], a '''transition function''' has several different meanings: * In [[topology]], a '''transition function''' is a [[homeomorphism]] from one coordinate [[~~chart~~Atlas (topology)\|chart]] to another. Given two charts (''U''<sub>''i''</sub>, φ<sub>''i''</sub>) and (''U''<sub>''j''</sub>, φ<sub>''j''</sub>) a transition [[function (mathematics)\|function]] normally takes the form ::<math>\phi_i\phi_j^{-1} : (U_i \cap U_j) \times F \to (U_i \cap U_j) \times F</math> :for some [[Set (mathematics)\|set]] ''F'' being covered by the [[topology]]. See [[fiber bundle]] and [[atlas (topology)]] for additional details. * In [[computing]], a '''transition function''' is the function that defines the state transitions of a [[Turing machine]] or a [[finite-state machine]]. {{mathdab}}[[Category:Homeomorphisms]]

Transition function: Difference between revisions