TRANSITION FUNCTION

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 (''U''_''i'', φ_''i'') and (''U''_''j'', φ_''j'') a transition function normally takes the form
::$phi\_iphi\_j^\{-1\}\; :\; (U\_i\; cap\; U\_j)\; imes\; F\; o\; (U\_i\; cap\; U\_j)\; imes\; F$
:for some 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 state machine.