Consider an evolutionary process that carries points of an initial state into
points of a final state. When the process is described by a vector field, the
tangents to the vector field define a set of lines which are Fibers projecting
into the Base of the final state. It is this visual feature of evolutionary
processes that gives the theory of Fiber bundles its utility in many physical
circumstances. The evolutionary process need not be singly paramatrized, and
moreover it need not be an element of a group.
Much of the current research in Fiber bundle theory is restricted to those cases
where the Fiber is an element of a group, and to when the Fiber "space" of
parameters is compact. However, such restrictions are not useful to the study of
open irreversible processes.