Remarks on Souslin properties and tree topologies
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- by William G. Fleissner PDF
- Proc. Amer. Math. Soc. 80 (1980), 320-326 Request permission
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
- Keith J. Devlin and Saharon Shelah, Souslin properties and tree topologies, Proc. London Math. Soc. (3) 39 (1979), no. 2, 237–252. MR 548979, DOI 10.1112/plms/s3-39.2.237
- William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4
- Mary Ellen Rudin, Countable paracompactness and Souslin’s problem, Canadian J. Math. 7 (1955), 543–547. MR 73155, DOI 10.4153/CJM-1955-058-8
- Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
Additional 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