Hereditarily weakly confluent induced mappings are homeomorphisms

• Autorzy: Janusz J. Charatonik , Włodzimierz J. Charatonik
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 75
• Numer: 2
• Strony: 195-203

Daty

wydano

1998

otrzymano

1996-10-09

poprawiono

1997-04-25

Twórcy

autor

Janusz J. Charatonik

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

autor

Włodzimierz J. Charatonik

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

Bibliografia

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• [7] H. Hosokawa, Induced mappings between hyperspaces II, ibid. 44 (1992), 1-7.
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• [9] H. Hosokawa, Induced mappings on hyperspaces II, ibid., to appear.
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• [12] S. B. Nadler, Jr., Hyperspaces of Sets, Dekker, 1978.