Abstract

It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) ->C(Y) is open, then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is open, then f is a homeomorphism. An example is given to show that local connectedness is essential in the result.

Department(s)

Mathematics and Statistics

Keywords and Phrases

Continuum; Induced Mapping; Monotone; Open

Library of Congress Subject Headings

Hyperspace

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 1999 American Mathematical Society, All rights reserved.

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