Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Openness of induced projections


Authors: Janusz J. Charatonik, Wlodzimierz J. Charatonik and Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 128 (2000), 3711-3714
MSC (2000): Primary 54B20, 54E40, 54F15, 54F50, 54F65
Published electronically: June 7, 2000
MathSciNet review: 1707141
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For continua $X$ and $Y$ it is shown that if the projection $f:X\times Y\to X$ has its induced mapping $C(f)$ open, then $X$ is $C^{*}$-smooth. As a corollary, a characterization of dendrites in these terms is obtained.


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

  • 1. J. J. Charatonik, W. J. Charatonik and A. Illanes, Openness of induced mappings, Topology Appl. 98 (1999), 67-80. CMP 99:17
  • 2. J. Grispolakis, Sam B. Nadler Jr., and E. D. Tymchatyn, Some properties of hyperspaces with applications to continua theory, Canad. J. Math. 31 (1979), no. 1, 197–210. MR 518720, 10.4153/CJM-1979-021-9
  • 3. Hiroshi Hosokawa, Induced mappings between hyperspaces. II, Bull. Tokyo Gakugei Univ. (4) 44 (1992), 1–7. MR 1193338
  • 4. Hiroshi Hosokawa, Induced mappings on hyperspaces, Tsukuba J. Math. 21 (1997), no. 1, 239–250. MR 1467235
  • 5. 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
  • 6. 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54B20, 54E40, 54F15, 54F50, 54F65

Retrieve articles in all journals with MSC (2000): 54B20, 54E40, 54F15, 54F50, 54F65


Additional Information

Janusz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland; Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: jjc@hera.math.uni.wroc.pl, jjc@gauss.matem.unam.mx

Wlodzimierz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland; Departamento de Matemáticas, Facultad de Ciencias, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Address at time of publication: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409-0020
Email: wjcharat@hera.math.uni.wroc.pl, wjcharat@lya.fciencias.unam.mx

Alejandro Illanes
Affiliation: Instituto de Matemátic as, UNAM, Circuito Exterior, Ciudad Universitaria, 04510 México, D. F., México
Email: illanes@gauss.matem.unam.mx

DOI: https://doi.org/10.1090/S0002-9939-00-05589-1
Keywords: $C^{*}$-smooth, continuum, dendrite, induced mapping, open, projection
Received by editor(s): February 2, 1999
Published electronically: June 7, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society