Open problems in topology

Pearl, Elliott

doi:10.1016/s0166-8641(03)00183-4

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Cited by 7 publications

(1 citation statement)

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“…Succinctly,

\mathcal {F}

induces a partition of

\mathcal {P}(U)

into large and small sets, respectively. Ultrafilters have found several important applications in Banach space theory [3, 38], topology [37, 52], and combinatorics [12, 67], among many others.…”

Section: Introductionmentioning

confidence: 99%

Negating the Galvin property

Tom

Garti

Poveda

2023

Journal of London Math Soc

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We investigate Galvin's property, a striking feature of the filter of closed unbounded subsets of an infinite cardinal. In particular, we continue the work of Abraham and Shelah (J. Symbolic Logic 51 (1986), no. 1, 180–189) by developing new methods to handle singular cardinals. In addition, the paper explores some new strengthenings of Galvin's property and analyzes their connections with other classical properties of filters.

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“…Succinctly,

\mathcal {F}

induces a partition of

\mathcal {P}(U)

into large and small sets, respectively. Ultrafilters have found several important applications in Banach space theory [3, 38], topology [37, 52], and combinatorics [12, 67], among many others.…”

Section: Introductionmentioning

confidence: 99%