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.
Recommended Citation
W. J. Charatonik, "Openness and Monotoneity of Induced Mappings," Proceedings of the American Mathematical Society, American Mathematical Society, Aug 1999.
The definitive version is available at https://doi.org/10.1090/S0002-9939-99-05135-7
Department(s)
Mathematics and Statistics
Keywords and Phrases
Continuum; Induced Mapping; Monotone; Open; Hyperspace
International Standard Serial Number (ISSN)
0002-9939
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 1999 American Mathematical Society, All rights reserved.
Publication Date
01 Aug 1999
