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Mappings on the dyadic solenoid

Jan M. Aarts, Robbert J. Fokkink (2003)

Commentationes Mathematicae Universitatis Carolinae

Answering an open problem in [3] we show that for an even number k , there exist no k to 1 mappings on the dyadic solenoid.

Monotone retractions and depth of continua

Janusz Jerzy Charatonik, Panayotis Spyrou (1994)

Archivum Mathematicum

It is shown that for every two countable ordinals α and β with α > β there exist λ -dendroids X and Y whose depths are α and β respectively, and a monotone retraction from X onto Y . Moreover, the continua X and Y can be either both arclike or both fans.

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