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Mapping hierarchy for dendrites

100%

Charatonik J. J., Charatonik W. J., Prajs J. R.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS 1. Introduction..................................................................5 2. Preliminaries................................................................6 3. Hierarchy of spaces.....................................................7 4. Dendrites.....................................................................9 5. Monotone and confluent mappings............................13 6. Open mappings ........................................................22 7. Problems ...................................................................51 References....................................................................51

Hereditarily weakly confluent induced mappings are homeomorphisms

66%

Charatonik J. J., Charatonik W. J.

Colloquium Mathematicum

1998

tom 75

nr 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.

Ograniczanie wyników

1 Colloquium Mathematicum

2 Charatonik J. J.

2 Charatonik W. J.

1 Prajs J. R.

1 1998

1 1994

Wyniki wyszukiwania

Mapping hierarchy for dendrites

Hereditarily weakly confluent induced mappings are homeomorphisms