is a mapping.
,
may not be connected. To use the theorems above,
must be connected. Therefore,
is decomposed into the union of several sets first. Furthermore, for each set of
,
F is decomposed into the union of several mappings
such that each
is connected. Then, Theorem 5.2 is applied to each
, then integrate them together.
In Section
5.3, the concept of the homotopically equivalent class is introduced. We now extend the concept to sets in general product spaces.