|
A short proof of nonhomogeneity of the pseudo-circle
Author(s):
Krystyna
Kuperberg;
Kevin
Gammon
Journal:
Proc. Amer. Math. Soc.
137
(2009),
1149-1152.
MSC (2000):
Primary 54F15, 54F50
Posted:
September 17, 2008
MathSciNet review:
2457457
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
The pseudo-circle is known to be nonhomogeneous. The original proofs of this fact were discovered independently by L. Fearnley and J. T. Rogers, Jr. The purpose of this paper is to provide an alternative, very short proof based on a result of D. Bellamy and W. Lewis.
References:
-
- 1.
- D.P. Bellamy and W. Lewis, An orientation reversing homeomorphism of the plane with invariant pseudo-arc, Proc. Amer. Math. Soc. 114 (1992), 1145-1149. MR 1092915 (92g:54047)
- 2.
- R.H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742. MR 0027144 (10:261a)
- 3.
- R.H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43-51. MR 0043451 (13:265b)
- 4.
- R.H. Bing, Each homogeneous nondegenerate chainable continuum is a pseudo-arc, Proc. Amer. Math. Soc. 10 (1959), 345-346 MR 0105072 (21:3818)
- 5.
- L. Fearnley, The pseudo-circle is unique, Bull. Amer. Math. Soc. 75 (1969), 398-401. MR 0246265 (39:7569)
- 6.
- L. Fearnley, The pseudo-circle is not homogeneous, Bull. Amer. Math. Soc. 75 (1969), 554-558. MR 0242126 (39:3460)
- 7.
- L. Fearnley, The pseudo-circle is unique, Trans. Amer. Math. Soc. 149 (1970), 45-64. MR 0261559 (41:6172)
- 8.
- C.L. Hagopian, The fixed-point property for almost chainable homogeneous continua, Illinois J. Math. 20 (1976), 650-652. MR 0418057 (54:6101)
- 9.
- S.T. Hu, Homotopy Theory, Academic Press, New York, 1959. MR 0106454 (21:5186)
- 10.
- J. Kennedy and J.T. Rogers, Jr., Orbits of the pseudocircle, Trans. Amer. Math. Soc. 296 (1986), 327-340. MR 837815 (87g:54076)
- 11.
- B. Knaster, Un continu dont tout sous-continu est indécomposable, Fund. Math. 3 (1922), 247-286.
- 12.
- K. Kuratowski, Topology, Vol. II, Academic Press, 1968. MR 0259835 (41:4467)
- 13.
- W. Lewis, Almost chainable homogeneous continua are chainable, Houston J. Math. 7 (1981), 373-377. MR 640978 (83a:54044)
- 14.
- W. Lewis, The pseudo-arc, Contemp. Math. 117, Amer. Math. Soc., Providence, RI, 1991, 103-123. MR 1112808 (92h:54046)
- 15.
- W. Lewis, The pseudo-arc, Bol. Soc. Mat. Mexicana 5 (1999), 25-77. MR 1692467 (2000f:54029)
- 16.
- E.E. Moise, An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc. 63 (1948), 581-594. MR 0025733 (10:56i)
- 17.
- J.T. Rogers, Jr., The pseudo-circle is not homogeneous, Trans. Amer. Math. Soc. 148 (1970), 417-428. MR 0256362 (41:1018)
- 18.
- J.T. Rogers, Jr., Homogeneous, separating plane continua are decomposable, Michigan Math. J. 28 (1981), 317-322. MR 629364 (83b:54045)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
54F15, 54F50
Retrieve articles in all Journals with
MSC (2000):
54F15, 54F50
Additional Information:
Krystyna
Kuperberg
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
Email:
kuperkm@auburn.edu
Kevin
Gammon
Affiliation:
Department of Mathematics and Statistics, Auburn University, Auburn, Alabama 36849
Email:
gammokb@auburn.edu
DOI:
10.1090/S0002-9939-08-09605-6
PII:
S 0002-9939(08)09605-6
Keywords:
pseudo-circle,
pseudo-arc,
homogeneous,
composant,
indecomposable continuum
Received by editor(s):
March 7, 2008
Posted:
September 17, 2008
Dedicated:
Dedicated to James T. Rogers, Jr., on the occasion of his 65th birthday
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2008,
American Mathematical Society
|
