Hart, Klaas Pieter; Junnila, Heikki; van Mill, Jan A Dowker group. (English) Zbl 0592.22001 Commentat. Math. Univ. Carol. 26, 799-810 (1985). In this note the authors give, in ZFC, an example of a normal topological group which is not countably paracompact. This is done by applying the B(X)-construction of the first and third author [Topology Appl. 20, 279- 287 (1985; Zbl 0577.22005)] to a suitable Dowker space X. The main difficulty is to assure that the semitopological group B(X), which is a Dowker space if all finite powers of X are normal, is in fact a topological group. To this end the authors replace in M. E. Rudin’s Dowker space X the cardinals \(\omega,\omega_ 1,\omega_ 2,..\). by a sequence of successive cardinals \(\alpha,\alpha^+,..\). (\(\alpha\geq \omega)\) and show (i) B(X) is a topological group for \(\alpha \geq 2^{\omega}\) (and hence a Dowker group), (ii) B(X) is not a topological group for \(\alpha^+<2^{\omega}\); for \(\alpha^+=2^{\omega}\) the problem is unsolved. Reviewer: V.Eberhardt Cited in 3 Documents MSC: 22A05 Structure of general topological groups 54G20 Counterexamples in general topology 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.) Keywords:counterexample; P-space; ZFC; normal topological group; countably paracompact; Dowker space; Dowker group Citations:Zbl 0577.22005 PDFBibTeX XMLCite \textit{K. P. Hart} et al., Commentat. Math. Univ. Carol. 26, 799--810 (1985; Zbl 0592.22001) Full Text: EuDML