Games and Metrisability of Manifolds - NZJM

New Zealand Journal of Mathematics

David Gauld¹  Abdul Mohamad²  Jiling Cao³  Sina Greenwood¹ 

[1] Department of MathematicsThe University of AucklandPrivate Bag 92019Auckland 1020NEW ZEALAND$$;Department of Mathematics and StatisticsSultan Qaboos UniversityP.O. Box 36MuscatSULTANATE OF OMAN$$;School of Computing and Mathematical SciencesAuckland University of TechnologyPrivate Bag 92006Auckland 1020NEW ZEALAND$$

关键词: Banach-Mazur game;    Choquet game;    Compact-open topology;    Manifold;    Metrisable;    Moving Off Property;    Strongly Baire;    Baire;    Volterra;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

Using topological games we investigate connections between properties of topological spaces and their spaces of continuous functions with the compact-open topology. This leads to new criteria for metrisability of a manifold. We show that a manifold M is metrisable if and only if a winning strategy applies to certain topological games played on Ck(M). We also show that M is metrisable if and only if Ck(M) is Baire, and even if and only if it is Volterra.

【 授权许可】

Unknown