Mappings between dendroids (fans) that (does not) preserve (non) contractibility

Abstract

Abstract. J. J. Charatonik formulated in 1991 the following problem: What are all mappings that preserve contractibility (noncontractibility) of dendroids? On the other hand, J. J. Charatonik, W. J. Charatonik, and S. Miklos asked in 1990 the following questions (among others related to contractibility): What kinds of confluent mappings preserve contractibility of fans? And what kinds of confluent mappings preserve non contractibility of fans? In this paper, we will show some partial answers to these questions. Additionally, we will consider these questions with other kinds of families of mappings.