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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 mappings


Authors: Janusz J. Charatonik and Pawel Krupski
Journal: Proc. Amer. Math. Soc. 132 (2004), 1211-1217
MSC (2000): Primary 54C60, 54C65, 54E40, 54F50
Published electronically: October 29, 2003
MathSciNet review: 2045440
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Abstract: It is shown that a metric continuum $X$ is a dendrite if and only if for every compact space (continuum) $Y$ and for every light confluent 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. As a corollary it follows that only dendrites have the lifting property with respect to light confluent mappings. Other classes of mappings $f$ are also discussed. This is a continuation of a previous study by the authors (2000), where open mappings $f$ were considered.


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Additional Information

Janusz J. Charatonik
Affiliation: Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: jjc@matem.unam.mx

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

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07270-8
PII: S 0002-9939(03)07270-8
Keywords: Confluent, continuum, dendrite, lifting, light, mapping, open
Received by editor(s): March 14, 2001
Received by editor(s) in revised form: February 4, 2002
Published electronically: October 29, 2003
Communicated by: Alan Dow
Article copyright: © Copyright 2003 American Mathematical Society