Hereditarily weakly confluent induced mappings are homeomorphisms

Volume 75 / 1998

Janusz Charatonik, Włodzimierz Charatonik Colloquium Mathematicum 75 (1998), 195-203 DOI: 10.4064/cm-75-2-195-203


For a given mapping f between continua we consider the induced mappings between the corresponding hyperspaces of closed subsets or of subcontinua. It is shown that if either of the two induced mappings is hereditarily weakly confluent (or hereditarily confluent, or hereditarily monotone, or atomic), then f is a homeomorphism, and consequently so are both the induced mappings. Similar results are obtained for mappings between cones over the domain and over the range continua.


  • Janusz Charatonik
  • Włodzimierz Charatonik

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