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Proceedings of the American Mathematical Society
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
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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.

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  • [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 (51 #1730)
  • [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 (41 #4467)

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Additional Information

PII: S 0002-9939(1984)0746103-4
Keywords: Graph, $ X$-space, locally connected continuum, hereditarily locally connected continuum, open mapping, retraction
Article copyright: © Copyright 1984 American Mathematical Society