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Full-Text Articles in Physical Sciences and 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.
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Openness And Monotoneity Of Induced Mappings, W. J. Charatonik
Mathematics and Statistics Faculty Research & Creative Works
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.