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.
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
Mathematics and Statistics
Keywords and Phrases
Continuum; Induced Mapping; Monotone; Open; Hyperspace
Article - Journal
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