View More View Less
  • 1 Vrije Universiteit Faculty of Sciences, Division of Mathematics De Boelelaan 1081a 1081 HV Amsterdam the Netherlands
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

We show that the cardinality of power homogeneous T 5 compacta X is bounded by 2 c ( X ) . This answers a question of J. van Mill, who proved this bound for homogeneous T 5 compacta. We further extend some results of I. Juhász, P. Nyikos and Z. Szentmiklóssy and as a corollary we prove that consistently every power homogeneous T 5 compactum is first countable. This improves a theorem of R. de la Vega who proved this consistency result for homogeneous T 5 compacta.

  • Arhangel’skiį, A. V. , The structure and classification of topological spaces and cardinal invariants, Uspekhi Mat. Nauk , 33 (1978), no. 6 (204), 29–84, 272. MR80i :54005

    Arhangel’skiį A. V. , 'The structure and classification of topological spaces and cardinal invariants ' (1978 ) 33 Uspekhi Mat. Nauk : 29 -84.

    • Search Google Scholar
  • Arhangel’skiį, A. V., van Mill, J. and Ridderbos, G. J. , A new bound on the cardinality of power homogeneous compacta, Houston Journal of Mathematics , 33 (2007), no. 3, 781–793. MR 2335735

    Ridderbos G. J. , 'A new bound on the cardinality of power homogeneous compacta ' (2007 ) 33 Houston Journal of Mathematics : 781 -793.

    • Search Google Scholar
  • Arhangel’skiį , A weak algebraic structure on topological spaces and cardinal invariants, Topology Proc. , 28 (2004), No. 1, 1–18, Spring Topology and Dynamical System Conference.

    Arhangel’skiį , 'A weak algebraic structure on topological spaces and cardinal invariants ' (2004 ) 28 Topology Proc. : 1 -18.

    • Search Google Scholar
  • Bella, A. , Remarks on the cardinality of a power homogeneous space, Comment. Math. Univ. Carolin. , 46 (2005), no. 3, 463–468. MR2006d :54003

    Bella A. , 'Remarks on the cardinality of a power homogeneous space ' (2005 ) 46 Comment. Math. Univ. Carolin. : 463 -468.

    • Search Google Scholar
  • Juhász, I. , Cardinal functions in topology-ten years later , Mathematical Centre Tracts, vol. 123, Mathematisch Centrum, Amsterdam, second ed., 1980. MR82a :54002

    Juhász I. , '', in Cardinal functions in topology-ten years later , (1980 ) -.

  • Juhász, I., Nyikos, P. and Szentmiklóssy, Z. , Cardinal restrictions on some homogeneous compacta, Proc. Amer. Math. Soc. , 133 (2005), no. 9, 2741–2750 (electronic). MR2006g :54006

    Szentmiklóssy Z. , 'Cardinal restrictions on some homogeneous compacta ' (2005 ) 133 Proc. Amer. Math. Soc. : 2741 -2750.

    • Search Google Scholar
  • Juhász, I. and Szentmiklóssy, Z. , Convergent free sequences in compact spaces, Proc. Amer. Math. Soc. , 116 (1992), no. 4, 1153–1160. MR93b :54024

    Szentmiklóssy Z. , 'Convergent free sequences in compact spaces ' (1992 ) 116 Proc. Amer. Math. Soc. : 1153 -1160.

    • Search Google Scholar
  • van Mill, J. , On the cardinality of power homogeneous compacta, Topology Appl. , 146/147 (2005), 421–428. MR2005j :54005

    Mill J. , 'On the cardinality of power homogeneous compacta ' (2005 ) 146/147 Topology Appl. : 421 -428.

    • Search Google Scholar
  • Ridderbos, G. J. , A characterization of power homogeneity, Topology Appl. , 155 (2008), 318–321. MR 2380269

    Ridderbos G. J. , 'A characterization of power homogeneity ' (2008 ) 155 Topology Appl. : 318 -321.

    • Search Google Scholar
  • Ridderbos, G. J ., On the cardinality of power homogeneous Hausdorr spaces, Fund. Math. , 192 (2006), 255–266. MR2007m :54004

    Ridderbos G. J. , 'On the cardinality of power homogeneous Hausdorr spaces ' (2006 ) 192 Fund. Math. : 255 -266.

    • Search Google Scholar
  • Ridderbos, G. J. , Power homogeneity in Topology , Doctoral Thesis, Vrije Universiteit Amsterdam (2007).

  • Šapirovskiį, B. È. , π-character and π-weight in bicompacta, Dokl. Akad. Nauk SSSR , 223 (1975), no. 4, 799–802. MR53 #14380

    Šapirovskiį B. È. , 'π-character and π-weight in bicompacta ' (1975 ) 223 Dokl. Akad. Nauk SSSR : 799 -802.

    • Search Google Scholar
  • Tall, F. D. , PFA(S)[S]: more mutually consistent topological consequences of PFA and V = L , in preparation.

  • Tall, F. D. , Normality versus collectionwise normality , Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 685–732. MR86m :54022

    Tall F. D. , '', in Normality versus collectionwise normality , (1984 ) -.

  • de la Vega, R. , A new bound on the cardinality of homogeneous compacta, Topology Appl. , 153 (2006), 2118–2123. MR2007e :54008

    Vega R. , 'A new bound on the cardinality of homogeneous compacta ' (2006 ) 153 Topology Appl. : 2118 -2123.

    • Search Google Scholar