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

$\phi _{i}\phi _{j}^{-1}:(U_{i}\cap U_{j})\times F\to (U_{i}\cap U_{j})\times F$

for some set F being covered by the topology. See fiber bundle and atlas (topology) for additional details.

• In computing, a transition function is the function that defines the state transitions of a Turing machine or a finite-state machine.