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Proceedings of the American Mathematical Society

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

 
 

 

There is a $Q$-set space in ZFC


Author: Zoltán T. Balogh
Journal: Proc. Amer. Math. Soc. 113 (1991), 557-561
MSC: Primary 54G20; Secondary 54H05
DOI: https://doi.org/10.1090/S0002-9939-1991-1077786-3
MathSciNet review: 1077786
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Abstract: It is shown that there is a regular ${T_1}$-space whose every subset is a ${G_\delta }$-set and yet the space is not $\sigma$-discrete.


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Keywords: <!– MATH ${G_\delta }$ –> <IMG WIDTH="30" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="${G_\delta }$">-set, <IMG WIDTH="18" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\sigma$">-discrete left-separated, elementary submodel
Article copyright: © Copyright 1991 American Mathematical Society