|
A hereditarily indecomposable tree-like continuum without the fixed point property
Author(s):
Piotr
Minc
Journal:
Trans. Amer. Math. Soc.
352
(2000),
643-654.
MSC (2000):
Primary 54F15;
Secondary 54H25
Posted:
September 17, 1999
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
A hereditarily indecomposable tree-like continuum without the fixed point property is constructed. The example answers a question of Knaster and Bellamy.
References:
- 1.
- H. Bell, On fixed point properties of plane continua, Trans. Amer. Math. Soc. 128 (1967), 539-548. MR 35:4888
- 2.
- D.P. Bellamy, A tree-like continuum without the fixed-point property, Houston J. Math. 6 (1980), 1-13. MR 81h:54039
- 3.
- -, The fixed point property in dimension one, in Continua with the Houston problem book (H. Cook et al., eds.), Marcel Dekker, New York, 1995, pp. 27-35. MR 96a:54056
- 4.
- R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742. MR 10:261a
- 5.
- K. Borsuk, A theorem on fixed points, Bull. Acad. Sci. Polon. 2 (1954), 17-20. MR 16:275h
- 6.
- H. Cook, W. T. Ingram and A. Lelek, A list of problems known as Houston Problem Book, in Continua with the Houston problem book (H. Cook et al., eds.), Marcel Dekker, New York, 1995, pp. 365-398. MR 96f:54042
- 7.
- L. Fearnley and D. G. Wright, Geometric realization of a Bellamy continuum, Bull. London Math. Soc. 25 (1993), 177-183. MR 94b:54095
- 8.
- J. B. Fugate and L. A. Mohler, A note on fixed points in tree-like continua, Topology Proc. 2 (1977), 457-460. MR 80k:54062
- 9.
- C. L. Hagopian, A fixed point theorem for plane continua, Bull. Amer. Math. Soc. 77 (1971), 351-354. MR 42:8469
- 10.
- -, Fixed points of plane continua, Rocky Mountain J. Math. 23 (1993), 119-186. MR 94h:54054
- 11.
- -, The fixed-point property for simply connected plane continua, Trans. Amer. Math. Soc. 348 (1996), 4525-4548. MR 97a:54047
- 12.
- -, The fixed point property for deformations of tree-like continua, Fund. Math. 155 (1998), 161-176. MR 99b:54046
- 13.
- G. W. Henderson, The pseudo-arc as an inverse limit with one binding map, Duke Math. J. 31 (1964), 421-425. MR 29:4039
- 14.
- S. Iliadis, Positions of continua in a plane and fixed points, Vestn. Moskov. Univ. 25 (1970), 66-70. MR 44:4726
- 15.
- B. Knaster, Un continu dont tout sous-continu est indécomposable, Fund. Math. 3 (1922), 247-286.
- 16.
- W. Lewis, Continuum theory problems, Topology Proc. 8 (1983), 361-394. MR 86a:54038
- 17.
- R. Ma\'{n}ka, Association and fixed points, Fund. Math. 91 (1976), 105-121. MR 54:1183
- 18.
- R. D. Mauldin (ed.), The Scottish Book: Mathematics from the Scottish Café, Birkhauser, Boston, 1981. MR 84m:00015
- 19.
- P. Minc, A fixed point theorem for weakly chainable plane continua, Trans. Amer. Math. Soc. 317 (1990), 303-312. MR 90d:54067
- 20.
- -, A tree-like continuum admitting fixed point free maps with arbitrarily small trajectories, Topology and its Appl. 46 (1992), 99-106. MR 94a:54108
- 21.
- -, A periodic points free homeomorphism of a tree-like continuum, Trans. Amer. Math. Soc. 348 (1996), 1487-1519. MR 96h:54029
- 22.
- -, A weakly chainable tree-like continuum without the fixed point property, Trans. Amer. Math. Soc. 351 (1999), 1109-1121. MR 99e:54024
- 23.
- -, A self map of a tree-like continuum with no invariant indecomposable subcontinuum, preprint.
- 24.
- P. Minc and W. R. R. Transue, A transitive map on
whose inverse limit is the pseudoarc, Proc. Amer. Math. Soc. 111 (1991), 1165-1170. MR 91g:54050 - 25.
- L.G. Oversteegen and J.T. Rogers, Jr., Tree-like continua as limits of cyclic graphs, Topology Proc. 4 (1979), 507-515. MR 82c:54032
- 26.
- -, An inverse limit description of an atriodic tree-like continuum and an induced map without a fixed point, Houston J. Math. 6 (1980), 549-564. MR 82j:54075
- 27.
- -, Fixed-point-free maps on tree-like continua, Topology and its Appl. 13 (1982), 85-95. MR 83b:54044
- 28.
- K. Sieklucki, On a class of plane acyclic continua with the fixed point property, Fund. Math. 63 (1968), 257-278. MR 39:2139
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(2000):
54F15,
54H25
Retrieve articles in all Journals with MSC
(2000):
54F15,
54H25
Additional Information:
Piotr
Minc
Affiliation:
Department of Mathematics, Auburn University, Auburn, Alabama 36849
Email:
mincpio@mail.auburn.edu
DOI:
10.1090/S0002-9947-99-02570-2
PII:
S 0002-9947(99)02570-2
Keywords:
Tree-like continuum,
hereditarily indecomposable,
fixed points
Received by editor(s):
September 19, 1997
Posted:
September 17, 1999
Additional Notes:
This research was supported in part by NSF grant # DMS-9505108.
Copyright of article:
Copyright
1999,
American Mathematical Society
|