The rank of the diagonal and submetrizability
Several topological properties lying between the submetrizability and the -diagonal property are studied. We are mostly interested in their relationship to each other and to the submetrizability. The first example of a Tychonoff space with a regular -diagonal but without a zero-set diagonal is given. The same example shows that a Tychonoff separable space with a regular -diagonal need not be submetrizable. We give a necessary and sufficient condition for submetrizability of a regular separable...