Schmidt games and Cantor winning sets

Research output: Working paperPreprint

Standard

Schmidt games and Cantor winning sets. / Simmons, David Samuel; Badziahin, Dzmitry; Harrap, Stephen; Nesharim, Erez.

arXiv, 2020.

Research output: Working paperPreprint

Harvard

Simmons, DS, Badziahin, D, Harrap, S & Nesharim, E 2020 'Schmidt games and Cantor winning sets' arXiv. <https://arxiv.org/abs/1804.06499>

APA

Simmons, D. S., Badziahin, D., Harrap, S., & Nesharim, E. (2020). Schmidt games and Cantor winning sets. arXiv. https://arxiv.org/abs/1804.06499

Vancouver

Simmons DS, Badziahin D, Harrap S, Nesharim E. Schmidt games and Cantor winning sets. arXiv. 2020 May 25.

Author

Simmons, David Samuel ; Badziahin, Dzmitry ; Harrap, Stephen ; Nesharim, Erez. / Schmidt games and Cantor winning sets. arXiv, 2020.

Bibtex - Download

@techreport{d701f5bb763047e696a0730f420a8480,
title = "Schmidt games and Cantor winning sets",
abstract = "Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of study. We survey the definitions of the most common variants and connections between them. A new game called the Cantor game is invented and helps with presenting a unifying framework. We prove surprising new results such as the coincidence of absolute winning and 1 Cantor winning in metric spaces, and the fact that 1/2 winning implies absolute winning for subsets of R, and we suggest a prototypical example of a Cantor winning set to show the ubiquity of such sets in metric number theory and ergodic theory.",
author = "Simmons, {David Samuel} and Dzmitry Badziahin and Stephen Harrap and Erez Nesharim",
year = "2020",
month = may,
day = "25",
language = "English",
publisher = "arXiv",
type = "WorkingPaper",
institution = "arXiv",

}

RIS (suitable for import to EndNote) - Download

TY - UNPB

T1 - Schmidt games and Cantor winning sets

AU - Simmons, David Samuel

AU - Badziahin, Dzmitry

AU - Harrap, Stephen

AU - Nesharim, Erez

PY - 2020/5/25

Y1 - 2020/5/25

N2 - Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of study. We survey the definitions of the most common variants and connections between them. A new game called the Cantor game is invented and helps with presenting a unifying framework. We prove surprising new results such as the coincidence of absolute winning and 1 Cantor winning in metric spaces, and the fact that 1/2 winning implies absolute winning for subsets of R, and we suggest a prototypical example of a Cantor winning set to show the ubiquity of such sets in metric number theory and ergodic theory.

AB - Schmidt games and the Cantor winning property give alternative notions of largeness, similar to the more standard notions of measure and category. Being intuitive, flexible, and applicable to recent research made them an active object of study. We survey the definitions of the most common variants and connections between them. A new game called the Cantor game is invented and helps with presenting a unifying framework. We prove surprising new results such as the coincidence of absolute winning and 1 Cantor winning in metric spaces, and the fact that 1/2 winning implies absolute winning for subsets of R, and we suggest a prototypical example of a Cantor winning set to show the ubiquity of such sets in metric number theory and ergodic theory.

M3 - Preprint

BT - Schmidt games and Cantor winning sets

PB - arXiv

ER -