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

 

Dendrites and light open mappings


Authors: Janusz J. Charatonik, Wlodzimierz J. Charatonik and Pawel Krupski
Journal: Proc. Amer. Math. Soc. 128 (2000), 1839-1843
MSC (1991): Primary 54C60, 54C65, 54E40, 54F50
Published electronically: February 25, 2000
MathSciNet review: 1787331
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Abstract: 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 $f: Y \to f(Y)$ such that $X \subset f(Y)$ there is a copy $X'$ of $X$ in $Y$ for which the restriction $f\vert X': X' \to X$ is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also 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, wjcharat@umr.edu

Pawel Krupski
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Email: krupski@hera.math.uni.wroc.pl

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05693-8
PII: S 0002-9939(00)05693-8
Keywords: Continuum, dendrite, light, mapping, multifunction, open, selection
Received by editor(s): June 2, 1997
Received by editor(s) in revised form: August 30, 1997
Published electronically: February 25, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society