P-Filters and the perfect set property

Jialiang He, Shuguo Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we prove that every non-meager P-filter F is a PSP(σ11)-filter (that is, A∩F has the perfect set property whenever A is an analytic subset of 2) and the filter product of a Ramsey ultrafilter and a P•2-point is a PSP(σ11)-ultrafilter. These theorems strengthen a result of Miller and answer some questions asked by Andrea Medini and David Milovich.

Original languageEnglish
Pages (from-to)12-19
Number of pages8
JournalTopology and its Applications
Volume162
Issue number1
DOIs
StatePublished - 1 Feb 2014
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by NSFC Grants # 10971149 and # 11271272 .

Funding

This work was supported by NSFC Grants # 10971149 and # 11271272 .

FundersFunder number
National Natural Science Foundation of China10971149, 11271272

    Keywords

    • Non-meager P-filter
    • P-point
    • PSP(σ11)-ultrafilter
    • P•2-point
    • Ramsey ultrafilter

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