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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Applications of a set-theoretic lemma
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by Gary Gruenhage PDF
Proc. Amer. Math. Soc. 92 (1984), 133-140 Request permission

Abstract:

A set-theoretic lemma is introduced and various applications are given, including: (1) a result of Erdös and Hajnal on the coloring number of a graph; (2) game characterizations of the coloring number of a graph; (3) K. Alster’s result that a point-countable collection of open, compact scattered spaces has a point-finite clopen refinement; (4) normal, locally compact, metacompact spaces which are scattered of finite height are paracompact.
References
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    • —, Covering properties on ${X^2}\backslash \Delta$, $W$-sets, and compact subsets of $\Sigma$-products, Topology Appl. (to appear).
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  • Franklin D. Tall, On the existence of normal metacompact Moore spaces which are not metrizable, Canadian J. Math. 26 (1974), 1–6. MR 377823, DOI 10.4153/CJM-1974-001-8
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 133-140
  • MSC: Primary 54D18; Secondary 04A20, 05C15
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0749905-3
  • MathSciNet review: 749905