On Topological Properties of the Hartman–Mycielski Functor

[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.

[学科分类] 数学（综合）

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