There is a paracompact Q-set space in ZFC

Balogh, Zoltan

doi:10.1090/S0002-9939-98-04426-8

There is a paracompact Q-set space in ZFC
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by Zoltan T. Balogh

Proc. Amer. Math. Soc. 126 (1998), 1827-1833

DOI: https://doi.org/10.1090/S0002-9939-98-04426-8

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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′skiǐ and D. Shakhmatov on cleavable spaces.

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