Accessible points of hereditarily decomposable chainable continua
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- by Piotr Minc and W. R. R. Transue PDF
- Trans. Amer. Math. Soc. 332 (1992), 711-727 Request permission
Abstract:
In this paper it is proven that a chainable continuum $X$ can be embedded in the plane in such a way that every point is accessible from its complement if and only if it is Suslinean. An example is shown of an hereditarily decomposable chainable continuum which cannot be embedded in the plane in such a way that each endpoint is accessible.References
- R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653–663. MR 43450
- J. B. Fugate, Decomposable chainable continua, Trans. Amer. Math. Soc. 123 (1966), 460–468. MR 196720, DOI 10.1090/S0002-9947-1966-0196720-1
- J. B. Fugate, A characterization of chainable continua, Canadian J. Math. 21 (1969), 383–393. MR 240785, DOI 10.4153/CJM-1969-040-x
- 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
- A. Lelek, On the Moore triodic theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 271–276. MR 148023 S. Mazurkiewicz, Sur les points accessibles des continus indécomposables, Fund. Math. 14 (1929), 107-115.
- Piotr Minc and W. R. R. Transue, Sarkovskiĭ’s theorem for hereditarily decomposable chainable continua, Trans. Amer. Math. Soc. 315 (1989), no. 1, 173–188. MR 965302, DOI 10.1090/S0002-9947-1989-0965302-9
- Lee Mohler, The depth of tranches in $\lambda$-dendroids, Proc. Amer. Math. Soc. 96 (1986), no. 4, 715–720. MR 826508, DOI 10.1090/S0002-9939-1986-0826508-5 R. L. Moore, Concerning triodic continua in the plane, Fund. Math. 13 (1929), 261-263.
- E. S. Thomas Jr., Monotone decompositions of irreducible continua, Rozprawy Mat. 50 (1966), 74. MR 196721 University of Houston Problem Book, (mimeographed notes).
- Gail S. Young Jr., A generalization of Moore’s theorem on simple triods, Bull. Amer. Math. Soc. 50 (1944), 714. MR 10967, DOI 10.1090/S0002-9904-1944-08216-5
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 332 (1992), 711-727
- MSC: Primary 54F15; Secondary 54C25
- DOI: https://doi.org/10.1090/S0002-9947-1992-1073777-2
- MathSciNet review: 1073777