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.
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 if there exists a surjection f ∈ F of X onto Y. We investigate the quasi-order 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 , and characterize spaces which can be...
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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