On topological properties of the Hartman--Mycielski functor

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 ($HX$, HM$Y$) is homeomorphic to the pair $(Q,\sigma)$ for each nondegenerated metrizable compactum $X$ and each dense $\sigma$-compact subset $Y$.