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* 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 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 [[fiber bundle]] for
* In [[computing]], a ''transition function'' is the function that defines the state transitions of a [[Turing machine]] or a [[state machine]].
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