Generic left-separated spaces and calibers
نویسنده
چکیده
In this paper we use a natural forcing to construct a left-separated topology on an arbitrary cardinal κ. The resulting left-separated space Xκ is also 0-dimensional T2, hereditarily Lindelöf, and countably tight. Moreover if κ is regular then d(Xκ) = κ, hence κ is not a caliber of Xκ, while all other uncountable regular cardinals are. This implies that some results of [A] and [JSz] are, consistently, sharp. We also prove it consistent that for every countable set A of uncountable regular cardinals there is a hereditarily Lindelöf T3 space X such that % = cf(%) > ω is a caliber of X exactly if % 6∈ A.
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