Layer-by-layer infinite iterations of some metrizable functors (Q750941)

The functors in this paper assign to each compact space X a compact space F(X), together with continuous mappings \(\eta_ X: X\to F(X)\) and \(\psi_ X: F(F(X))\to F(X)\). These mappings give rise to three sequences with respective limits \(F^{\omega}(X)\), \(F^{++}(X)\) and \(F^+(X)\). In many cases, the triple formed by these limits is homeomorphic to the triple (Q,s,rint Q) where Q denotes the Hilbert cube. The author extends this result of Fedorchuk to so-called parametrizable functors of which \({\mathcal P}(X)\), the space of all probability measures on X, is typical.