One primitive topological property is the concept of the number of parts, or
components, of a set. If the number of parts changes during an evolutionary
process, then the topology of the initial state is not the same as the topology
of the final state. The number of parts is not the only topological property
that can change during an evolutionary process. A simple intuitive description
of topological evolution can be expressed in terms of the operation of cutting
into separable parts, and pasting of parts together. Although both processes
effect topological change, the cutting process is a discontinuous
process, where the pasting process is continuous. As demonstrated
herein, Cartan's exterior calculus permits analytic progress to be made in the
understanding of irreversible processes that involve continous topological
change. As of this date (with notable exceptions  see the discussion on
defects and singularities) the discontinuous processes have been little studied
in terms of Cartan's techniques.
