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
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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.
- Version 2002-06-19_11 (10p) 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},
mrnumber = {1991801},
mrclass = {54A25 (03E35)},
doi = {10.1016/S0166-8641(02)00367-X},
note = {\href{https://arxiv.org/abs/math/0212027}{arXiv: math/0212027}},
arxiv_number = {math/0212027}
}