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 is the intersection of countably many partition complete subsets of , then is partition complete. (2) If is -scattered, where is the class of all partition complete spaces, then is partition complete. (3) If is a primitive set in a -scattered space , then is the intersection of countably many -scattered subsets of . (4) The partition completeness is perfect and preserved by open maps.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0929013-2

Keywords:
Partition complete space,
sieve complete space,
-scattered space,
exhaustive sieve,
open presieve,
primitive set,
perfect mapping,
open mapping,
topological game

Article copyright:
© Copyright 1988
American Mathematical Society