On projections and limit mappings of inverse systems of compact spaces
type: Item
instance of: scholarly article
title: On projections and limit mappings of inverse systems of compact spaces
zbMATH Open document ID: 0532.54007
DOI: 10.1016/0166-8641(83)90002-0
published in: Topology and its Applications
publication date: 1983-01-01T00:00:00Z
review text: The authors consider mappings between inverse systems over arbitrary directed sets of indices and the corresponding induced mappings between limit spaces. The spaces in the systems are assumed to be compact Hausdorff and the mappings in the system are continuous and onto. The authors proved that the induced maps are monotone, confluent or weakly confluent if the mappings between systems consist of monotone, confluent or weakly confluent mappings, respectively. The case of monotone maps was considered by \textit{C. E. Capel} [Duke Math. J. 21,233-245 (1954; Zbl 0055.412)]. In fact the authors proved more detailed versions of theorems listed above taking into consideration mappings which are monotone, confluent or weakly confluent with respect to given points in their domains (for monotone mappings) or in their ranges (for confluent and weakly confluent ones). In the case of weakly confluent mappings the proofs rely upon some hyperspace techniques from \textit{S. B. Nadler}'s book ''Hyperspaces of sets'' (1978; Zbl 0432.54007).
Mathematics Subject Classification ID: 54B35
zbMATH DE Number: 3844594
zbMATH Keywords: monotone, confluent or weakly confluent mappings
zbMATH Keywords: hyperspace techniques
author: Janusz J. Charatonik
author: Włodzimierz J. Charatonik
reviewed by: Jerzy Mioduszewski
MaRDI profile type: Publication
full work available at URL: 0166-8641(83)90002-0
OpenAlex ID: W2021479385
cites work: Inverse limit spaces
cites work: Confluent mappings and unicoherence of continua
cites work: Q4150804
cites work: Some properties of the induced map
cites work: Q5665902
cites work: Q5676808
cites work: Q3869981
cites work: Limit mappings and projections of inverse systems
description: scientific article; zbMATH DE number 3844594