Title

Hereditarily Weakly Confluent Induced Mappings Are Homeomorphisms

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

atriodic; semi-confluent; hereditary; confluent; atomic; homeomorphism; cone; weakly confluent; monotone; hyperspace; joining; continuum; confluent mapping

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1998 Polskiej Akademii Nauk, Instytut Matematyczny, All rights reserved.

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