Remarks on Souslin Properties and Tree Topologies

Abstract

We investigate the relation of Souslin (antichain) properties of trees and tree topologies. One result extends a result of Devlin and Shelah by proving, within ZFC, the equivalence of four properties for <o,-trees-collectionwise normal, normal and collectionwise Hausdorff, property y, and antichain normal and collectionwise Hausdorff. A second result is the construction, assuming V = L, of an Aronszajn tree which is not countably metacompact. Third, we show that no tree can be a Dowker space.