A mapping I: X -+ Y between continua X and Y is called an MO-mapping provided that it can be represented as the composition of two mappings, II : X -+ Z and I2 : Z -+ Y. such that II is open and I2 is monotone. Induced MO-mappings, 21 and C(f), between hyperspaces are studied. In particular an example is con-structed of an open mapping I : [0.1] ---+ [0.1 j for which C(fJ is not an MO-mapping. This answers two questions asked by H. Hoso-kawa.
J. J. Charatonik and W. J. Charatonik, "Induced MO-mappings," Tsukuba Journal of Mathematics, University of Tsukuba, Jan 1999.
Mathematics and Statistics
Keywords and Phrases
hyperspace; induced mapping; monotone; MO-mapping; open
Article - Journal
© 1999 University of Tsukuba, All rights reserved.
01 Jan 1999