On Topological Properties of the Hartman–Mycielski Functor

Proceedings Mathematical Sciences

Taras Radul²  DuÅ¡an RepovÅ¡¹ 

[1] Institute for Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska , Ljubljana, Slovenia 00$$;Departmento de Matematicas, Facultad de Cs. Fisicas y Matematicas, Universidad de Concepcion, Casilla 0-C, Concepcion, Chile$$

关键词: Hilbert cube;    Hartman–Mycielski construction;    equiconnected space;    normal functor;    metrizable compactum;    absolute retract.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We investigate some topological properties of a normal functor 𝐻 introduced earlier by Radul which is some functorial compactification of the Hartman–Mycielski construction HM. We prove that the pair (𝐻𝑋, 𝐻𝑀𝑌) is homeomorphic to the pair $(mathcal{Q}, 𝜎)$ for each nondegenerated metrizable compactum 𝑋 and each dense 𝜎-compact subset 𝑌.

【 授权许可】

Unknown