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Countable Fréchet Boolean groups: An independence result

Published online by Cambridge University Press:  12 March 2014

Jörg Brendle  and
Michael Hrušák
Jörg Brendle
Affiliation:
Graduate School of Engineering, Kobe University, Rokko-Dai 1-1, Nada-Ku, Kobe 657-8501, Japan, E-mail: [email protected]
Michael Hrušák
Affiliation:
Graduate School of Engineering, Kobe University, Rokko-Dai 1-1, Nada-Ku, Kobe 657-8501, Japan, E-mail: [email protected]
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Abstract

It is relatively consistent with ZFC that every countable FUfin space of weight ℵ1 is metrizable. This provides a partial answer to a question of G. Gruenhage and P. Szeptycki [GS1].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 3 , September 2009 , pp. 1061 - 1068
Copyright
Copyright © Association for Symbolic Logic 2009

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References

REFERENCES

[Ar]Arhangel'skii, A. V., Classes of topological groups, Russian Mathematical Surveys, vol. 36 (1981), pp. 151–174.CrossRefGoogle Scholar
[Brl]Brendle, J., Van Douwen's diagram for dense sets of rationals, Annals of Pure and Applied Logic, vol. 143 (2006), pp. 54–69.CrossRefGoogle Scholar
[Br2]Brendle, J., Independence for distributivity numbers, Algebra, logic, set theory. Festschrift für Ulrich Felgner zum 65. Geburtstag (Löwe, B., editor), Studies in Logic, vol. 4, College Publications, London, 2007, pp. 63–84.Google Scholar
[Do]Dow, A., Two classes of Fréchet–Urysohn spaces, Proceedings of the American Mathematical Society, vol. 108 (1990), pp. 241–247.Google Scholar
[GN]Gerlits, J. and Nagy, Zs., Some properties of C(X), I, Topology and its Applications, vol. 14 (1982), pp. 151–161.CrossRefGoogle Scholar
[GS1]Gruenhage, G. and Szeptycki, P. J., Fréchet–Urysohn for finite sets, Topology and its Applications, vol. 151 (2005), pp. 238–259.CrossRefGoogle Scholar
[GS2]Gruenhage, G. and Szeptycki, P. J., Fréchet–Urysohn for finite sets, II, Topology and its Applications, vol. 154 (2007), pp. 2856–2872.CrossRefGoogle Scholar
[HG]Hrušák, M. and García-Ferreira, S., Ordering MAD families a la Katětov, this Journal, vol. 68 (2003), pp. 1337–1353.Google Scholar
[HR]Hrušák, M. and Ramos-García, U. A., Pre-compact topologies on countable abelian groups, in preparation, 2008.Google Scholar
[HZ]Hrušák, M. and Zapletal, J., Forcing with quotients, Archive for Mathematical Logic, vol. 47 (2008), pp. 719–739.CrossRefGoogle Scholar
[MT]Moore, J. T. and Todorăević, S., The metrization problem for Fréchet groups, Open problems in topology II (Pearl, E., editor), Elsevier, 2007, pp. 201–206.CrossRefGoogle Scholar
[Ny1]Nyikos, P., Subsets of ωω and the Fréchet–Urysohn and αi-properties, Topology and its Applications, vol. 48 (1992), pp. 91–116.CrossRefGoogle Scholar
[Ny2]Nyikos, P., The Cantor tree and the Fréchet–Urysohn property, Annals of the New York Academy of Sciences, vol. 552 (1989), pp. 109–123.CrossRefGoogle Scholar
[RS]Reznichenko, E. and Sipacheva, O., Fréchet–Urysohn type properties in topological spaces, groups and locally convex vector spaces, Moscow University Mathematics Bulletin, vol. 54 (1999), pp. 33–38.Google Scholar
[Si]Sipacheva, O., Spaces Fréchet–Urysohn with respect to families of subsets, Topology and its Applications, vol. 121 (2002), pp. 305–317.CrossRefGoogle Scholar