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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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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  • Hiroshi Hosokawa, Induced mappings on hyperspaces, Tsukuba J. Math. 21 (1997), no. 1, 239–250. MR 1467235, DOI 10.21099/tkbjm/1496163175
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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