INTERSECTION TOPOLOGIES WITH RESPECT TO SEPARABLE GO-SPACES AND THE COUNTABLE ORDINALS

Given two topologies, T-1 and T-2, on the same set X, the intersection topology with respect to T-1 and T-2 is the topology with basis {U1 boolean AND U-2 : U-1 is an element of T-1, U-2 is an element of T-2}. Equivalently, T is the join of T-1 and T-2 in the lattice of topologies on the set X. Following the work of Reed concerning intersection topologies with respect to the real line and the countable ordinals, Kunen made an extensive investigation of normality, perfectness and omega(1)-compactness in this class of topologies. We demonstrate that the majority of his results generalise to the intersection topology with respect to an arbitrary separable GO-space and omega(1), employing a well-behaved second countable subtopology of the separable GO-space.