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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 (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]] ''F'' being covered by the [[topology]]. See [[Atlas (topology)]] for additional details.
* In [[computing]], a '''transition function''' is the function that defines the state transitions of a [[Turing machine]] or a [[state machine]].
{{disambig}}
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