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 ω 1 {\omega _1} -trees-collectionwise normal, normal and collectionwise Hausdorff, property γ \gamma , and antichain normal and collectionwise Hausdorff. A second result is the construction, assuming V = L V = L , of an Aronszajn tree which is not countably metacompact. Third, we show that no tree can be a Dowker space.
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