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Proceedings of the American Mathematical Society

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Martin's axiom implies that de Caux's space is countably metacompact


Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 80 (1980), 495-498
MSC: Primary 54D15; Secondary 03E50, 54A35
DOI: https://doi.org/10.1090/S0002-9939-1980-0581013-3
MathSciNet review: 581013
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Abstract: De Caux defined a space $ S(\mathcal{L})$ and, assuming $ \clubsuit $, showed that $ S(\mathcal{L})$ is normal but not countably metacompact. We assume $ \mathrm{MA}_{\omega_1}$ and show that $ S(\mathcal{L})$ is countably metacompact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0581013-3
Keywords: Club, Martin's Axiom, Dowker space
Article copyright: © Copyright 1980 American Mathematical Society