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 | References | Similar Articles | Additional Information
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