Title

Openness of Induced Mappings

Abstract

Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X→Y the induced mapping C(f):C(X)→C(Y) is open, then f is a homeomorphism. It is shown that, besides hereditarily locally connected continua, all fans have this property, while some Cartesian products do not have it. If f:X×Y→X denotes the natural projection, then openness of C(f) implies that X is hereditarily unicoherent. The equivalence holds for dendrites. Some new characterizations of these curves are obtained.

Department(s)

Mathematics and Statistics

Keywords and Phrases

continuum; induced mapping; open

Library of Congress Subject Headings

Dendrites
Hyperspace

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1999 Elsevier, All rights reserved.

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