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 and, assuming , showed that is normal but not countably metacompact. We assume and show that is countably metacompact.

**[dC]**P. de Caux,*A collectionwise normal weakly*-*refinable Dowker space which is neither irreducible nor realcompact*, Topology Proceedings**1**(1976), 67-78.**[ER]**P. Erdös and R. Rado,*A partition calculus in set theory*, Bull. Amer. Math. Soc.**62**(1956), 427-489. MR**0081864 (18:458a)****[F]**W. Fleissner,*Applications of stationary sets in topology*, Surveys in General Topology (G. Reed, Ed.), Academic Press, New York, 1980, pp. 163-183. MR**564102 (81b:54007)****[N]**P. Nyikos,*A topological Litmus paper strip*, Notices Amer. Math. Soc.**26**(1979), A-478.**[R]**M. E. Rudin,*Lectures on set theoretic topology*, CBMS Regional Conf. Ser. Math., vol. 23, Amer. Math. Soc., Providence, R. I., 1975. MR**0367886 (51:4128)****[Wa]**M. L. Wage,*Almost disjoint sets and Martin's axiom*, J. Symbolic Logic**44**(1979), 313-318. MR**540662 (80j:03079)****[W]**N. Williams,*Combinatorial set theory*, North-Holland, Amsterdam, 1977.

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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