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Marion Scheepers

  1. Remarks on countable tightness.

    Wed, 01/25/2012 - 15:01 — SomNambul
    Authors: Marion Scheepers
    Subjects: General Topology
    Abstract

    Countable tightness may be destroyed by countably closed forcing. We
    characterize the indestructibility of countable tightness under countably
    closed forcing by combinatorial statements similar to the ones Tall used to
    characterize indestructibility of the Lindelof property under countably closed
    forcing. We consider the behavior of countable tightness in generic extensions
    obtained by adding Cohen reals. We show that HFD's are indestructibly countably
    tight.

  2. Lindelof indestructibility, topological games and selection principles.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: Marion Scheepers, Franklin D. Tall
    Subjects: General Topology
    Abstract

    Arhangel'skii proved that if a first countable Hausdorff space is Lindel\"of,
    then its cardinality is at most $2^{\aleph_0}$. Such a clean upper bound for
    Lindel\"of spaces in the larger class of spaces whose points are ${\sf
    G}_{\delta}$ has been more elusive. In this paper we continue the agenda
    started in F.D. Tall, On the cardinality of Lindel\"of spaces with points
    $G_{\delta}$, Topology and its Applications 63 (1995), 21 - 38, of considering
    the cardinality problem for spaces satisfying stronger versions of the
    Lindel\"of property.

  3. Lindelof indestructibility, topological games and selection principles.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: Marion Scheepers, Franklin D. Tall
    Subjects: General Topology
    Abstract

    Arhangel'skii proved that if a first countable Hausdorff space is Lindel\"of,
    then its cardinality is at most $2^{\aleph_0}$. Such a clean upper bound for
    Lindel\"of spaces in the larger class of spaces whose points are ${\sf
    G}_{\delta}$ has been more elusive. In this paper we continue the agenda
    started in F.D. Tall, On the cardinality of Lindel\"of spaces with points
    $G_{\delta}$, Topology and its Applications 63 (1995), 21 - 38, of considering
    the cardinality problem for spaces satisfying stronger versions of the
    Lindel\"of property.

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