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Proceedings of the American Mathematical Society

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



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
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?)

  • [1] H. Cook, On subsets of indecomposable continua, Colloq. Math. 13 (1964), 37–43. MR 0178456
  • [2] W. Dębski and E. D. Tymchatyn, Composant-like decompositions of spaces, Fund. Math. 140 (1991), no. 1, 69–78. MR 1139088
  • [3] J. Krasinkiewicz, On internal composants of indecomposable plane continua, Fund. Math. 84 (1974), no. 3, 255–263. MR 0339101
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  • [5] S. Mazurkiewicz, Sur les points accessibles des continues indécomposables, Fund. Math. 14 (1929), 107-115.

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Article copyright: © Copyright 1987 American Mathematical Society