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Applications of a set-theoretic lemma


Author: Gary Gruenhage
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0749905-3
Article copyright: © Copyright 1984 American Mathematical Society

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