Kurepa trees and topological non-reflection

Citations of this article
Mendeley users who have this article in their library.
Get full text


A property P of a structure S does not reflect if no substructure of S of smaller cardinality than S has the property. If for a given property P there is such an S of cardinality κ, we say that P does not reflect at κ. We undertake a fine analysis of Kurepa trees which results in defining canonical topological and combinatorial structures associated with the tree which possess a remarkably wide range of nonreflecting properties providing new constructions and solutions of open problems in topology. The most interesting results show that many known properties may not reflect at any fixed singular cardinal of uncountable cofinality. The topological properties we consider vary from normality, collectionwise Hausdorff property to metrizablity and many others. The combinatorial properties are related to stationary reflection. © 2004 Elsevier B.V. All rights reserved.




Koszmider, P. (2005). Kurepa trees and topological non-reflection. Topology and Its Applications, 151(1-3 SPEC. ISS.), 77–98. https://doi.org/10.1016/j.topol.2003.08.033

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free