It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.
J. J. Charatonik et al., "Dendrites and Light Open Mappings," Proceedings of the American Mathematical Society, American Mathematical Society, Feb 2000.
The definitive version is available at https://doi.org/10.1090/S0002-9939-00-05693-8
Mathematics and Statistics
Keywords and Phrases
Continuum; Mapping; Multifunction; Open; Selection; Dendrites; Light
Article - Journal
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