# Sh:369

• Goldstern, M., Judah, H. I., & Shelah, S. (1991). A regular topological space having no closed subsets of cardinality \aleph_2. Proc. Amer. Math. Soc., 111(4), 1151–1159.
• Abstract:
We show in ZFC that there is a regular (even zerodimensional) topological space of size > \aleph_2 in which there are no closed sets of size \aleph_2. The proof starts by noticing that if \beta\omega does not work, then we can use a \diamondsuit.
• published version (10p)
Bib entry
@article{Sh:369,
author = {Goldstern, Martin and Judah, Haim I. and Shelah, Saharon},
title = {{A regular topological space having no closed subsets of cardinality $\aleph_2$}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {111},
number = {4},
year = {1991},
pages = {1151--1159},
issn = {0002-9939},
mrnumber = {1052572},
mrclass = {54A25 (03E50 03E75)},
doi = {10.2307/2048582}
}