Remarks on countable tightness

Details Remarks on countable tightness Remarks on countable tightness

2012-01-24

arxiv.org/abs/1201.4909v1

Mathematics

General Topology

12 pages

Scientific paper

Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize indestructibility of the Lindelof property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that HFD's are indestructibly countably tight.

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