External equivalence classes in decompositions of spaces
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- by W. Dębski and E. D. Tymchatyn PDF
- Proc. Amer. Math. Soc. 100 (1987), 781-784 Request permission
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
- H. Cook, On subsets of indecomposable continua, Colloq. Math. 13 (1964), 37–43. MR 178456, DOI 10.4064/cm-13-1-37-43
- W. Dębski and E. D. Tymchatyn, Composant-like decompositions of spaces, Fund. Math. 140 (1991), no. 1, 69–78. MR 1139088, DOI 10.4064/fm-140-1-69-78
- J. Krasinkiewicz, On internal composants of indecomposable plane continua, Fund. Math. 84 (1974), no. 3, 255–263. MR 339101, DOI 10.4064/fm-84-3-255-263 K. Kuratowski, Topology. II, Academic Press, New York, 1968. S. Mazurkiewicz, Sur les points accessibles des continues indécomposables, Fund. Math. 14 (1929), 107-115.
Additional Information
- © Copyright 1987 American Mathematical Society
- 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