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Full-Text Articles in Mathematics
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Mathematics and Statistics Faculty Research & Creative Works
For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Mathematics and Statistics Faculty Research & Creative Works
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.