On topological properties of the Hartman--Mycielski functor

There is no monad based on Hartman-Mycielski functor

We show that there is no monad based on the normal functor $H$ introduced earlier by Radul which is a certain functorial compactification of the Hartman-Mycielski construction $HM$.

Hartman-Mycielski functor of non-metrizable compacta

We investigate some topological properties of a normal functor $H$ introduced earlier by Radul which is a certain functorial compactification of the Hartman-Mycielski construction $HM$. We show that $H$ is open and find the condition when $HX$ is an absolute retract homeomorphic to the Tychonov cube.

The construction of Hartman-Mycielski in topological gyrogroups

The concept of gyrogroups is a generalization of groups which do not explicitly have associativity. Recently, Wattanapan et al consider the construction of Hartman-Mycielski in strongly topological gyrogroups. In this paper, we extend their results in topological gyrogroups. We mainly, among other results, prove that every Hausdorff topological gyrogroup $G$ can be embedded as a closed subgyrogroup of a Hausdorff path-connected and locally path-connected topological gyrogroup $G^\bullet$.

拓扑MV-代数中的Hartman-Mycielski构造

The Hartman--Mycielski construction in topological MV-algebras

本文对任意Hausdorff拓扑MV-代数A，构造了其到道路连通、局部道路连通拓扑MV-代数A^•的闭子代数的自然拓扑同构，并证明了连续实值有界函数的扩展及连续同态的延拓性质。