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


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
Published electronically: August 3, 1999
MathSciNet review: 1641665
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Abstract | References | Similar Articles | Additional Information

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?)

  • 1. J. J. Charatonik and W. J. Charatonik, Lightness of induced mappings, Tsukuba J. Math. 22 (1998), 179-192. CMP 98:16
  • 2. Hiroshi Hosokawa, Induced mappings between hyperspaces. II, Bull. Tokyo Gakugei Univ. (4) 44 (1992), 1–7. MR 1193338 (94a:54036)
  • 3. Hiroshi Hosokawa, Induced mappings on hyperspaces, Tsukuba J. Math. 21 (1997), no. 1, 239–250. MR 1467235 (98f:54011)
  • 4. K. Kuratowski, Topology. Vol. II, New edition, revised and augmented. Translated from the French by A. Kirkor, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe Polish Scientific Publishers, Warsaw, 1968. MR 0259835 (41 #4467)
  • 5. Sam B. Nadler Jr., Hyperspaces of sets, Marcel Dekker, Inc., New York-Basel, 1978. A text with research questions; Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49. MR 0500811 (58 #18330)
  • 6. Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943 (32 #425)

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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

PII: S 0002-9939(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

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