Minimal non-invertible transformations of solenoids

Volume 127 / 2012

Dariusz Tywoniuk Colloquium Mathematicum 127 (2012), 243-252 MSC: Primary 37B05; Secondary 54H20. DOI: 10.4064/cm127-2-7


We construct a continuous non-invertible minimal transformation of an arbitrary solenoid. Since solenoids, as all other compact monothetic groups, also admit minimal homeomorphisms, our result allows one to classify solenoids among continua admitting both invertible and non-invertible continuous minimal maps.


  • Dariusz TywoniukInstitute of Mathematics and Computer Science
    Wrocław University of Technology
    50-372 Wrocław, Poland

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