Article ID Journal Published Year Pages File Type
4658888 Topology and its Applications 2013 6 Pages PDF
Abstract

Let AA denote the Alexandroff–Urysohn double arrow space. We prove the following results: (a) A×2ω is not countable dense homogeneous; (b) Aω is not countable dense homogeneous; (c) AA has exactly cc types of countable dense subsets. These results answer questions by Arhangelʼskiĭ, Hrušák and van Mill.

Keywords
Related Topics
Physical Sciences and Engineering Mathematics Geometry and Topology
Preview
Countable dense homogeneity and the double arrow space
Authors
,