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Strongly chaotic dendrites

J. CharatonikW. Charatonik — 1996

Colloquium Mathematicae

The concept of a strongly chaotic space is introduced, and its relations to chaotic, rigid and strongly rigid spaces are studied. Some sufficient as well as necessary conditions are shown for a dendrite to be strongly chaotic.

Mapping hierarchy for dendrites

AbstractLet a family S of spaces and a class F of mappings between members of S be given. For two spaces X and Y in S we define Y F X if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order F in the family of dendrites, where F is one of the following classes of mappings: retractions, monotone, open, confluent or weakly confluent mappings. In particular, we investigate minimal and maximal elements, chains and antichains in the quasi-order F , and characterize spaces which can be...

Confluent mappings of fans

CONTENTS1. Introduction.......................................................52. Preliminaries ....................................................83. General properties .........................................114. Mappings onto fans........................................145. Mappings onto an arc.....................................206. A characterization of the top...........................277. Open mappings and their lightness................288. Inverse limits...................................................399....

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