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There is a paracompact Q-set space in ZFC

Author: Zoltan T. Balogh
Journal: Proc. Amer. Math. Soc. 126 (1998), 1827-1833
MSC (1991): Primary 54Dxx
MathSciNet review: 1459106
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Abstract: We construct a paracompact space $QX$ such that every subset of $QX$ is an $F_{\sigma }$-set, yet $QX$ is not $\sigma $-discrete. We will construct our space not to have a $G_{\delta }$-diagonal, which answers questions of A.V. Arhangel'skii and D. Shakhmatov on cleavable spaces.

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Zoltan T. Balogh
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45058

Keywords: Paracompact, Q-set space, $G_{\delta }$-diagonal, cleavable
Received by editor(s): August 24, 1995
Additional Notes: Research supported by NSF Grant DMS-9108476.
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1998 American Mathematical Society