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. DOI: 10.2307/2048582 MR: 1052572
• 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)

@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}
}