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ArticleOriginal scientific text

Title

Hereditarily weakly confluent induced mappings are homeomorphisms

Authors 1, 1

Affiliations

  1. Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

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.

Keywords

ENG
atriodic, semi-confluent, hereditary, confluent, atomic, homeomorphism, cone, weakly confluent, monotone, hyperspace, joining, continuum

Bibliography

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Colloquium Mathematicum
1998/75/2
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Pages:
195-203
Main language of publication
English
Received
1996-10-09
Accepted
1997-04-25
Published
1998
Exact and natural sciences