Proceedings of the American Mathematical Society

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



Open retractions on locally connected continua

Author: S. Miklos
Journal: Proc. Amer. Math. Soc. 91 (1984), 630-632
MSC: Primary 54C10; Secondary 54C15, 54F15, 54F25
MathSciNet review: 746103
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a locally connected continuum $ X$ admits open retractions onto each of its subcontinua if and only if $ X$ is either an arc or a simple closed curve.

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

  • [1] R. W. FitzGerald, Connected sets with a finite disconnection property, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 139–173. MR 0365478
  • [2] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C10, 54C15, 54F15, 54F25

Retrieve articles in all journals with MSC: 54C10, 54C15, 54F15, 54F25

Additional Information

Keywords: Graph, $ X$-space, locally connected continuum, hereditarily locally connected continuum, open mapping, retraction
Article copyright: © Copyright 1984 American Mathematical Society