Remarks on Countable Tightness
Document Type
Article
Publication Date
1-1-2014
Abstract
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 Lindelöf property under countably closed forcing. We consider the behavior of countable tightness in generic extensions obtained by adding Cohen reals. We show that certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are further explored.
Publication Information
Scheepers, Marion. (2014). "Remarks on Countable Tightness". Topology and its Applications, 161407-432. https://doi.org/10.1016/j.topol.2013.11.001