Layer-by-layer infinite iterations of some metrizable functors
type: Item
instance of: scholarly article
title: Layer-by-layer infinite iterations of some metrizable functors
zbMATH Open document ID: 0714.54024
author: L. L. Oridoroga
published in: Moscow University Mathematics Bulletin
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18C15
zbMATH DE Number: 4175972
zbMATH Keywords: hyperspaces
zbMATH Keywords: monadic functors
zbMATH Keywords: compact space
zbMATH Keywords: probability measures
reviewed by: J. Sonner
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4175972