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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Complete exhaustive sieves and games


Authors: Rastislav Telgársky and Howard H. Wicke
Journal: Proc. Amer. Math. Soc. 102 (1988), 737-744
MSC: Primary 54E99; Secondary 54D99
DOI: https://doi.org/10.1090/S0002-9939-1988-0929013-2
MathSciNet review: 929013
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Abstract: Properties of completely regular spaces with complete exhaustive sieves are studied using the equivalent notion of partition complete spaces and associated games. Among others the following results are proved. (1) If $ X$ is the intersection of countably many partition complete subsets of $ Y$, then $ X$ is partition complete. (2) If $ X$ is $ K$-scattered, where $ K$ is the class of all partition complete spaces, then $ X$ is partition complete. (3) If $ X$ is a primitive set in a $ C$-scattered space $ Y$, then $ X$ is the intersection of countably many $ C$-scattered subsets of $ Y$. (4) The partition completeness is perfect and preserved by open maps.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0929013-2
Keywords: Partition complete space, sieve complete space, $ K$-scattered space, exhaustive sieve, open presieve, primitive set, perfect mapping, open mapping, topological game
Article copyright: © Copyright 1988 American Mathematical Society