The interval topology on T/sub 1/-lattices

摘要

The main purpose of the paper is to study under which conditions the interval topology on a T/sub 1/-lattice may be Hausdorff. The authors show that for a T/sub 1/-lattice L, the interval topology on L cannot be Hausdorff except in the extreme case that L is isomorphic to the power set of some set X. Similarly, for a T/sub 1/-space (X, /spl part/(X)), the interval topology on /spl part/(X) cannot be Hausdorff except in the extreme case that (X. /spl part/(X)) is discrete.