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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Openness of induced projections


Authors: Janusz J. Charatonik, Wlodzimierz J. Charatonik and Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 128 (2000), 3711-3714
MSC (2000): Primary 54B20, 54E40, 54F15, 54F50, 54F65
Published electronically: June 7, 2000
MathSciNet review: 1707141
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Abstract: For continua $X$ and $Y$ it is shown that if the projection $f:X\times Y\to X$ has its induced mapping $C(f)$ open, then $X$ is $C^{*}$-smooth. As a corollary, a characterization of dendrites in these terms is obtained.


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Additional Information

Janusz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland; Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: jjc@hera.math.uni.wroc.pl, jjc@gauss.matem.unam.mx

Wlodzimierz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland; Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Address at time of publication: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409-0020
Email: wjcharat@hera.math.uni.wroc.pl, wjcharat@lya.fciencias.unam.mx

Alejandro Illanes
Affiliation: Instituto de Matemátic as, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: illanes@gauss.matem.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05589-1
PII: S 0002-9939(00)05589-1
Keywords: $C^{*}$-smooth, continuum, dendrite, induced mapping, open, projection
Received by editor(s): February 2, 1999
Published electronically: June 7, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society