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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Remarks on Souslin properties and tree topologies


Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 80 (1980), 320-326
MSC: Primary 54F05; Secondary 54D15
DOI: https://doi.org/10.1090/S0002-9939-1980-0577767-2
MathSciNet review: 577767
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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 $ {\omega _1}$-trees-collectionwise normal, normal and collectionwise Hausdorff, property $ \gamma $, 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.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0577767-2
Article copyright: © Copyright 1980 American Mathematical Society