# 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)

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}, doi = {10.2307/2048582}, mrclass = {54A25 (03E50 03E75)}, mrnumber = {1052572}, mrreviewer = {Judith Roitman}, doi = {10.2307/2048582} }