PMEA and first countable, countably paracompact spaces

Author:
Dennis K. Burke

Journal:
Proc. Amer. Math. Soc. **92** (1984), 455-460

MSC:
Primary 54D15; Secondary 54D18, 54E30

DOI:
https://doi.org/10.1090/S0002-9939-1984-0759673-7

MathSciNet review:
759673

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Abstract: The Product Measure Extension Axiom is used to prove a "-expandable" type property for first countable, countably paracompact (countably metacompact) spaces. Among other results, it follows (under PMEA) that countably paracompact Moore spaces are metrizable, and first countable, countably paracompact Hausdorff spaces are strongly collectionwise normal with respect to compact sets.

**[A]**C. E. Aull,*A note on countably paracompact spaces and metrization*, Proc. Amer. Math. Soc.**16**(1965), 1316-1317. MR**0185575 (32:3039)****[**W. G. Fleissner,**F**]*Separation properties in Moore spaces*, Fund. Math.**98**(1978), 279-286. MR**0478111 (57:17600)****[**-,**F**]*The normal Moore space conjecture and large cardinals*, Handbook of Set-Theoretic Topology (to appear).**[M]**J. Mack,*Countable paracompactness and weak normal properties*, Trans. Amer. Math. Soc.**148**(1970), 265-272. MR**0259856 (41:4485)****[N]**P. J. Nyikos,*A provisional solution to the normal Moore space problem*, Proc. Amer. Math. Soc.**78**(1980). MR**553389 (81k:54044)****[T]**F. D. Tall,*Normality versus collectionwise normality*, Handbook of Set-Theoretic Topology (to appear). MR**776634 (86m:54022)****[W]**W. S. Watson,*Applications of set theory to general topology*, Thesis, University of Toronto, 1982.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0759673-7

Keywords:
Product Measure Extension Axiom,
countably paracompact,
countably metacompact,
Moore space,
collectionwise normal

Article copyright:
© Copyright 1984
American Mathematical Society