In this paper X is a non empty topological space and A , B are subsets of X . B is proper. B is dense.
B is nowhere dense.
B is everywhere dense. Let X be a non trivial non empty topological space and D be a non empty proper subset of the carrier of X . Let X be a non trivial non empty topological space and Y 1 be a proper non empty subspace of X . Y 2 of X such that Y 1 and Y 2 constitute a decomposition.