### Generic left-separated spaces and calibers

by Juhasz and Shelah. [JuSh:795]

Topology and its Applications, 2003

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
Lindel{o}f, 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 Lindel{o}f
T_3 space X such that varrho =cf(varrho) > omega is a caliber
of X exactly if varrho not in A .

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