Ir al contenido

Documat


A note on rank 2 diagonals

  • Bella, Angelo [1] ; Spadaro, Santi [1]
    1. [1] University of Catania

      University of Catania

      Catania, Italia

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 21, Nº. 1, 2020, págs. 81-85
  • Idioma: inglés
  • DOI: 10.4995/agt.2020.12065
  • Enlaces
  • Resumen
    • We solve two questions regarding spaces with a ($G_\delta$)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos regarding weakly Lindel\"of spaces with a $G_\delta$-diagonal of rank 2 and the other is a question of Arhangel'skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.

  • Referencias bibliográficas
    • A. V. Arhangel'skii and A. Bella, The diagonal of a first-countable paratopological groups, submetrizability and related results, Appl....
    • A. V. Arhangel'skii and R. Z. Buzyakova, The rank of the diagonal and submetrizability, Comment. Math. Univ. Carolinae 47 (2006), 585-597.
    • A. Bella, Remarks on the metrizability degree, Boll. Union. Mat. Ital. 1-3 (1987), 391-396.
    • D. Basile, A. Bella and G. J. Ridderbos, Weak extent, submetrizability and diagonal degrees, Houston J. Math. 40 (2014), 255-266.
    • M. Bell, J. Ginsburg and G. Woods, Cardinal inequalities for topological spaces involving the weak Lindelöf number, Pacific J. Math. 79 (1978),...
    • A. Bella and S. Spadaro, Cardinal invariants of cellular Lindelöf spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019),...
    • R. Buzyakova, Cardinalities of ccc spaces with regular Gδ-diagonals, Topology Appl. 153 (2006), 1696-1698. https://doi.org/10.1016/j.topol.2005.06.004
    • J. Chaber, Conditions which imply compactness in countably compact spaces, Bull. Acad. Pol. Sci. Ser. Math. 24 (1976), 993-998.
    • E. K. van Douwen and M. Reed, On chain conditions in Moore spaces II, Topology Appl. 39 (1991), 65-69. https://doi.org/10.1016/0166-8641(91)90076-X
    • J. Ginsburg and R. G. Woods, A cardinal inequality for topological spaces involving closed discrete sets, Proc. Amer. Math. Soc. 64 (1977),...
    • J. van Mill, V. V. Tkachuk and R. G. Wilson, Classes defined by stars and neighbourhood assignments, Topology Appl. 154, no. 10 (2007), 2127-2134....
    • R. Engelking, General Topology, Heldermann Verlag, Berlin, second ed., 1989.
    • D. Shakhmatov, No upper bound for cardinalities of Tychonoff C.C.C. spaces with a Gδ diagonal exist (an answer to J. Ginsburg and R.G. Woods'...
    • V. Sneider, Continuous images of Souslin and Borel sets: metrization theorems, Dokl. Acad. Nauk USSR, 50 (1945), 77-79.
    • V. Uspenskij, A large Fσ-discrete Fréchet space having the Souslin property, Comment. Math. Univ. Carolinae 25 (1984), 257-260.
    • W.-F. Xuan and Y.-K. Song, Dually properties and cardinal inequalities, Topology Appl. 234 (2018), 1-6. https://doi.org/10.1016/j.topol.2017.11.002
    • P. Zenor, On spaces with regular Gδ-diagonals, Pacific J. Math. 40 (1972), 959-963. https://doi.org/10.2140/pjm.1972.40.759

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno