Openness and monotoneity of induced mappings
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- by Włodzimierz J. Charatonik PDF
- Proc. Amer. Math. Soc. 127 (1999), 3729-3731 Request permission
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
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Additional Information
- Włodzimierz 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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1641665