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Mapping theorems on -spaces

Masami Sakai (2008)

Commentationes Mathematicae Universitatis Carolinae

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.

Mappings related to confluence

Janusz Jerzy Charatonik (1996)

Archivum Mathematicum

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.

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