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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Open retractions on locally connected continua
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by S. Miklos PDF
Proc. Amer. Math. Soc. 91 (1984), 630-632 Request permission

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
  • 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
  • K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 630-632
  • MSC: Primary 54C10; Secondary 54C15, 54F15, 54F25
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0746103-4
  • MathSciNet review: 746103