Skip to main content Accessibility help
×
Home

Countable Fréchet Boolean groups: An independence result

  • Jörg Brendle (a1) and Michael Hrušák (a1)

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].

Copyright

References

Hide All
[Ar]Arhangel'skii, A. V., Classes of topological groups, Russian Mathematical Surveys, vol. 36 (1981), pp. 151174.
[Brl]Brendle, J., Van Douwen's diagram for dense sets of rationals, Annals of Pure and Applied Logic, vol. 143 (2006), pp. 5469.
[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. 6384.
[Do]Dow, A., Two classes of Fréchet–Urysohn spaces, Proceedings of the American Mathematical Society, vol. 108 (1990), pp. 241247.
[GN]Gerlits, J. and Nagy, Zs., Some properties of C(X), I, Topology and its Applications, vol. 14 (1982), pp. 151161.
[GS1]Gruenhage, G. and Szeptycki, P. J., Fréchet–Urysohn for finite sets, Topology and its Applications, vol. 151 (2005), pp. 238259.
[GS2]Gruenhage, G. and Szeptycki, P. J., Fréchet–Urysohn for finite sets, II, Topology and its Applications, vol. 154 (2007), pp. 28562872.
[HG]Hrušák, M. and García-Ferreira, S., Ordering MAD families a la Katětov, this Journal, vol. 68 (2003), pp. 13371353.
[HR]Hrušák, M. and Ramos-García, U. A., Pre-compact topologies on countable abelian groups, in preparation, 2008.
[HZ]Hrušák, M. and Zapletal, J., Forcing with quotients, Archive for Mathematical Logic, vol. 47 (2008), pp. 719739.
[MT]Moore, J. T. and Todorăević, S., The metrization problem for Fréchet groups, Open problems in topology II (Pearl, E., editor), Elsevier, 2007, pp. 201206.
[Ny1]Nyikos, P., Subsets of ωω and the Fréchet–Urysohn and αi-properties, Topology and its Applications, vol. 48 (1992), pp. 91116.
[Ny2]Nyikos, P., The Cantor tree and the Fréchet–Urysohn property, Annals of the New York Academy of Sciences, vol. 552 (1989), pp. 109123.
[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. 3338.
[Si]Sipacheva, O., Spaces Fréchet–Urysohn with respect to families of subsets, Topology and its Applications, vol. 121 (2002), pp. 305317.

Related content

Powered by UNSILO

Countable Fréchet Boolean groups: An independence result

  • Jörg Brendle (a1) and Michael Hrušák (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.