Mikhail Tkachenko
A countably cellular topological group all of whose countable subsets are closed need not be \mathbb{R}-factorizable

Comment.Math.Univ.Carolin. 64,1 (2023) 127-135.

Abstract: We construct a Hausdorff topological group G such that \aleph_1 is a precalibre of G (hence, G has countable cellularity), all countable subsets of G are closed and C-embedded in G, but G is not \mathbb{R}-factorizable. This solves Problem 8.6.3 from the book ``Topological Groups and Related Structures" (2008) in the negative.

Keywords: \mathbb{R}-factorizable; cellularity; C-embedded; Sorgenfrey line; P-group; Dieudonné completion; Hewitt-Nachbin completion; Bohr topology

DOI: DOI 10.14712/1213-7243.2023.016
AMS Subject Classification: 22A05 54H11 54D30 54G20