Let X be a non empty topological space. Let A be a subset of the carrier of X . Suppose A it. Let V be a neighbourhood of A . W holds B W .
G is a neighbourhood of t .
The trivial decomposition of X is an upper semi-continuous decomposition of X . Let X be a topological space and let I 1 be a subspace of X . Let X be a topological space. Note that there exists a subspace of X which is strict and closed. Let us consider X .