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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Remarks on Souslin properties and tree topologies
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by William G. Fleissner
Proc. Amer. Math. Soc. 80 (1980), 320-326
DOI: https://doi.org/10.1090/S0002-9939-1980-0577767-2

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.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • 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