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Openness and monotoneity of induced mappings


Author: Wlodzimierz J. Charatonik
Journal: Proc. Amer. Math. Soc. 127 (1999), 3729-3731
MSC (1991): Primary 54B20, 54F15, 54E40
DOI: https://doi.org/10.1090/S0002-9939-99-05135-7
Published electronically: August 3, 1999
MathSciNet review: 1641665
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Abstract: It is shown that for locally connected continuum $X$ if the induced mapping $C(f): C(X) \to C(Y)$ 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.


References [Enhancements On Off] (What's this?)

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Additional Information

Wlodzimierz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland; Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: wjcharat@hera.math.uni.wroc.pl, wjcharat@lya.fciencias.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-99-05135-7
Keywords: Continuum, hyperspace, induced mapping, open, monotone
Received by editor(s): June 16, 1997
Received by editor(s) in revised form: January 4, 1998
Published electronically: August 3, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society