On projections and limit mappings of inverse systems of compact spaces
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).
monotone, confluent or weakly confluent mappings
scientific article; zbMATH DE number 3844594