# Sh:795

- Juhász, I., & Shelah, S. (2003).
*Generic left-separated spaces and calibers*. Topology Appl.,**132**(2), 103–108. arXiv: math/0212027 DOI: 10.1016/S0166-8641(02)00367-X MR: 1991801 -
Abstract:

We use a natural forcing to construct a left-separated topology on an arbitrary cardinal \kappa. The resulting left-separated space X_\kappa is also 0-dimensional T_2, hereditarily Lindelöf, and countably tight. Moreover if \kappa is regular then d(X_\kappa)=\kappa, hence \kappa is not a caliber of X_\kappa, while all other uncountable regular cardinals are.We also prove it consistent that for every countable set A of uncountable regular cardinals there is a hereditarily Lindelöf T_3 space X such that \varrho=cf(\varrho) >\omega is a caliber of X exactly if \varrho\not\in A.

- published version (6p)

Bib entry

@article{Sh:795, author = {Juh{\'a}sz, Istv{\'a}n and Shelah, Saharon}, title = {{Generic left-separated spaces and calibers}}, journal = {Topology Appl.}, fjournal = {Topology and its Applications}, volume = {132}, number = {2}, year = {2003}, pages = {103--108}, issn = {0166-8641}, doi = {10.1016/S0166-8641(02)00367-X}, mrclass = {54A25 (03E35)}, mrnumber = {1991801}, mrreviewer = {Norbert Brunner}, doi = {10.1016/S0166-8641(02)00367-X}, note = {\href{https://arxiv.org/abs/math/0212027}{arXiv: math/0212027}}, arxiv_number = {math/0212027} }