Applications of Pixley-Roy hyperspaces to Scheepers' conjecture on special subsets of reals

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400213
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kanagawa University
• Principal Investigator: SAKAI MASAMI 神奈川大学, 理学部, 教授 (60215598)
• Co-Investigator(Renkei-kenkyūsha): KADA Masaru 大阪府立大学, 理学研究科, 准教授 (00312447) ; OTA Haruto 静岡大学, 教育学部, 教授 (40126769)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: Pixley-Roy hyperspace

Outline of Final Research Achievements

Concerning Scheepers’ conjecture on special subsets of the real line and pseudo-normal convergence of continuous functions in a function space Cp(X) with the topology of pointwise convergence, we tried to answer the conjecture in view of Pixley-Roy hyperspaces. As a result, we obtained　the　following。(1) we gave , for　a　Pixley-Roy hyperspace PR(X), a　sufficient and　necessary　condition　for PR(X) to be weakly Hurewicz; (2) we answered, in the negative, Scheepers' question "Is every Lindelof space weakly Menger?", and as a byproduct, we answered, also in the negative, Wingers' question "Does every Lindelof space have a dense Menger subspace?".

Free Research Field

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