Accessible points of hereditarily decomposable chainable continua

Minc, Piotr; Transue, W. R. R.

doi:10.1090/S0002-9947-1992-1073777-2

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

Sur les points accessibles des continus indécomposables

14

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

Concerning triodic continua in the plane

13

E. S. Thomas Jr., Monotone decompositions of irreducible continua, Rozprawy Mat. 50 (1966), 74. MR 196721
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