Hereditarily Weakly Confluent Induced Mappings Are Homeomorphisms
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.
J. J. Charatonik and W. J. Charatonik, "Hereditarily Weakly Confluent Induced Mappings Are Homeomorphisms," Colloquium Mathematicae, Polskiej Akademii Nauk, Instytut Matematyczny, Jan 1998.
Mathematics and Statistics
Keywords and Phrases
atriodic; semi-confluent; hereditary; confluent; atomic; homeomorphism; cone; weakly confluent; monotone; hyperspace; joining; continuum; confluent mapping
Article - Journal
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