Partition axioms and lattice - equivalence of topological spaces

The purpose of this paper is to introduce new space structures Do1, Dv1/2and D1 which we shall refer to as partition axioms and prove that two Do-spaces are lattice-equivalent if and only if their T0 identifications are homeomorphic. As a consequence, we have that every cardinal preserving lattice-equivalence between two D1/2 -spaces are induced by a homeomorphism, and a result of Thron (1962) saying that two TD-spaces are lattice-equivalent if they are homeomorphic also follows.

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