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
This is the published version, also available here: http://www.dx.doi.org/10.1090/S0002-9939-1980-0577767-2. First published in Proceedings of the AMS in 1980, published by the American Mathematical Society.
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