Magill-type theorems for mappings.
In this paper we improve some mapping theorems on -spaces. For instance we show that an -space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an -space is preserved by a closed and open map.
Necessary and sufficient conditions are found in the paper for a mapping between continua to be monotone, confluent, semi-confluent, joining, weakly confluent and pseudo-confluent. Three lists of these conditions are presented. Two are formulated in terms of components and of quasi-components, respectively, of connected closed subsets of the range space, while the third one in terms of connectedness between subsets of the domain space. Some basic relations concerning these concepts are studied.