Openness of Induced Mappings
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.
J. J. Charatonik et al., "Openness of Induced Mappings," Topology and its Applications, Elsevier, Nov 1999.
The definitive version is available at http://dx.doi.org/10.1016/S0166-8641(99)00042-5
Mathematics and Statistics
Keywords and Phrases
Continuum; Induced Mapping; Open; Dendrites; Hyperspace
Article - Journal
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