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arXiv · math/0212027

Generic left-separated spaces and calibers

Istvan Juhász·Saharon Shelah
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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 Lindelof, 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 Lindelof T_3 space X such that rho=cf(rho)>omega is a caliber of X exactly if rho not in A.

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Istvan Juhász, Saharon Shelah. 2002-12-02. Generic left-separated spaces and calibers. https://arxiv.org/abs/math/0212027

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