Intervals in the lattices of zero-dimensional and of regular topologies
by
David McIntyre
University of Auckland

We will discuss the question of determining which finite lattices can occur as the collection of all zero-dimensional (resp. regular) topologies between two Hausdorff and zero-dimensional (resp. Hausdorff and regular) topologies. In the zero-dimensional case, only lattices of the form 2ⁿ can occur, whereas we give an example of two T₃ topologies with exactly one regular topology between them.

Date received: September 7, 2000