Consequences of axioms 0 and 1 Consequences of axioms 0, 1 and 2 Consequences of axioms 0, 1, 2, 3 and 5 Consequences of axioms 0 and 1-5 Upper semi-continuous collections Consequences of axioms $0, 1, 2, 3, 4, 5_1, 5_2, 6$ and $7$ Concerning topological equivalence and the introduction of distance Appendix Bibliography Glossary.