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Proceedings of the American Mathematical Society

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External equivalence classes in decompositions of spaces


Authors: W. Dębski and E. D. Tymchatyn
Journal: Proc. Amer. Math. Soc. 100 (1987), 781-784
MSC: Primary 54B15; Secondary 54F20
DOI: https://doi.org/10.1090/S0002-9939-1987-0894454-8
MathSciNet review: 894454
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Abstract: Let $ X$ be an indecomposable continuum in the plane. Krasinkiewicz has shown that the union of the external composants of $ X$ is a first category $ {F_\sigma }$ set in $ X$. We give extensions of this theorem to quite general decompositions of a space $ X$ embedded in a locally connected ambient space $ Y$.


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

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  • [2] W. Debski and E. D. Tymchatyn, Composant-like decompositions of spaces (to appear). MR 1139088 (93d:54046)
  • [3] J. Krasinkiewicz, On internal composants of indecomposable plane continua, Fund. Math. 84 (1974), 255-263. MR 0339101 (49:3864)
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  • [5] S. Mazurkiewicz, Sur les points accessibles des continues indécomposables, Fund. Math. 14 (1929), 107-115.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0894454-8
Article copyright: © Copyright 1987 American Mathematical Society

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