112 research outputs found

    Measurable cardinals and the cardinality of Lindel\"of spaces

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    If it is consistent that there is a measurable cardinal, then it is consistent that all points g-delta Rothberger spaces have "small" cardinality.Comment: 9 pag

    Remarks on countable tightness

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    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 certain classes of well-studied topological spaces are indestructibly countably tight. Stronger versions of countable tightness, including selective versions of separability, are further explored.Comment: Extended from 12 pages to 23 pages. Newly extended to 27 page

    Rothberger bounded groups and Ramsey theory

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    We show that: 1. Rothberger bounded subgroups of sigma-compact groups are characterized by Ramseyan partition relations. 2. For each uncountable cardinal κ\kappa there is a T0{\sf T}_0 topological group of cardinality κ\kappa such that ONE has a winning strategy in the point-open game on the group and the group is not a subspace of any sigma-compact space. 3. For each uncountable cardinal κ\kappa there is a T0{\sf T}_0 topological group of cardinality κ\kappa such that ONE has a winning strategy in the point-open game on the group and the group is \sigma-compact.Comment: 11 page

    Baire spaces and infinite games

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    It is well known that if the nonempty player of the Banach-Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box topology. The converse of this implication may be true also: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.Comment: 21 page

    Selection principles and countable dimension

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    We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.Comment: 10 page
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