|
Accessible points of hereditarily decomposable chainable continua
Authors:
Piotr Minc and W. R. R. Transue
Journal:
Trans. Amer. Math. Soc. 332 (1992), 711-727
MSC:
Primary 54F15; Secondary 54C25
MathSciNet review:
1073777
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: In this paper it is proven that a chainable continuum  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.
- [1]
R.
H. Bing, Snake-like continua, Duke Math. J.
18 (1951), 653–663. MR 0043450
(13,265a)
- [2]
J.
B. Fugate, Decomposable chainable
continua, Trans. Amer. Math. Soc. 123 (1966), 460–468. MR 0196720
(33 #4906), http://dx.doi.org/10.1090/S0002-9947-1966-0196720-1
- [3]
J.
B. Fugate, A characterization of chainable continua, Canad. J.
Math. 21 (1969), 383–393. MR 0240785
(39 #2130)
- [4]
K.
Kuratowski, Topology. Vol. II, New edition, revised and
augmented. Translated from the French by A. Kirkor, Academic Press, New
York, 1968. MR
0259835 (41 #4467)
- [5]
A.
Lelek, On the Moore triodic theorem, Bull. Acad. Polon. Sci.
Sér. Sci. Math. Astronom. Phys. 8 (1960),
271–276. MR 0148023
(26 #5533)
- [6]
S. Mazurkiewicz, Sur les points accessibles des continus indécomposables, Fund. Math. 14 (1929), 107-115.
- [7]
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
(89m:54054), http://dx.doi.org/10.1090/S0002-9947-1989-0965302-9
- [8]
Lee
Mohler, The depth of tranches in
𝜆-dendroids, Proc. Amer. Math. Soc.
96 (1986), no. 4,
715–720. MR
826508 (87g:54081), http://dx.doi.org/10.1090/S0002-9939-1986-0826508-5
- [9]
R. L. Moore, Concerning triodic continua in the plane, Fund. Math. 13 (1929), 261-263.
- [10]
E.
S. Thomas Jr., Monotone decompositions of irreducible
continua, Rozprawy Mat. 50 (1966), 74. MR 0196721
(33 #4907)
- [11]
University of Houston Problem Book, (mimeographed notes).
- [12]
Gail
S. Young Jr., A generalization of Moore’s
theorem on simple triods, Bull. Amer. Math.
Soc. 50 (1944), 714.
MR
0010967 (6,96c), http://dx.doi.org/10.1090/S0002-9904-1944-08216-5
- [1]
- R. H. Bing, Snake-line continua, Duke Math. J. 18 (1951), 653-663. MR 0043450 (13:265a)
- [2]
- J. B. Fugate, Decomposable chainable continua, Trans. Amer. Math. Soc. 123 (1966), 460-468. MR 0196720 (33:4906)
- [3]
- -, A characterization of chainable continua, Canad. J. Math. 21 (1969), 383-393. MR 0240785 (39:2130)
- [4]
- K. Kuratowski, Topology, Vol. II, Academic Press, New York and Polish Scientific Publishers, Warsaw, 1968. MR 0259835 (41:4467)
- [5]
- A. Lelek, On the Moore triodic theorem, Bull. Acad. Polon. Sci. 7 (1960), 271-276. MR 0148023 (26:5533)
- [6]
- S. Mazurkiewicz, Sur les points accessibles des continus indécomposables, Fund. Math. 14 (1929), 107-115.
- [7]
- P. Minc and W. R. R. Transue, Sarkovskii's theorem for hereditarily decomposable chainable continua, Trans. Amer. Math. Soc. 315 (1989), 173-188. MR 965302 (89m:54054)
- [8]
- L. Mohler, The depth of tranches in
 -dendroids, Proc. Amer. Math. Soc. 96 (1986), 715-720. MR 826508 (87g:54081)
- [9]
- R. L. Moore, Concerning triodic continua in the plane, Fund. Math. 13 (1929), 261-263.
- [10]
- E. S. Thomas, Jr., Monotone decompositions of irreducible continua, Rozprawy Mat. 50 (1960). MR 0196721 (33:4907)
- [11]
- University of Houston Problem Book, (mimeographed notes).
- [12]
- G. S. Young, Jr., A generalization of Moore's theorem on simple triods, Bull. Amer. Math. Soc. 50 (1944), 714. MR 0010967 (6:96c)
Similar Articles
Retrieve articles in Transactions of the American Mathematical Society
with MSC:
54F15,
54C25
Retrieve articles in all journals
with MSC:
54F15,
54C25
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1992-1073777-2
PII:
S 0002-9947(1992)1073777-2
Keywords:
Accessible points,
hereditarily decomposable,
chainable continuum,
Suslinean continuum
Article copyright:
© Copyright 1992 American Mathematical Society
|
