Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A continuous circle of pseudo-arcs
filling up the annulus

Author: Janusz R. Prajs
Journal: Trans. Amer. Math. Soc. 352 (2000), 1743-1757
MSC (1991): Primary 54F15; Secondary 54F50, 54B15
Published electronically: July 1, 1999
MathSciNet review: 1608498
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove an early announcement by Knaster on a decomposition of the plane. Then we establish an announcement by Anderson saying that the plane annulus admits a continuous decomposition into pseudo-arcs such that the quotient space is a simple closed curve. This provides a new plane curve, ``a selectible circle of pseudo-arcs", and answers some questions of Lewis.

References [Enhancements On Off] (What's this?)

  • 1. R.D. Anderson, On collections of pseudo-arcs, Abstract 337t, Bull. Amer. Math. Soc. 56(1950), 350.
  • 2. R. D. Anderson and G. Choquet, A plane continuum no two of whose nondegenerate subcontinua are homeomorphic: an application of inverse limits, Proc. Amer. Math. Soc. 10(1959), 347-353. MR 21:3819
  • 3. R. H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1(1951), 43-51. MR 13:265b
  • 4. R. H. Bing and F. B. Jones, Another homogeneous plane continuum, Trans. Amer. Math. Soc. 90(1959), 171-192. MR 20:7251
  • 5. M. Brown, Continuous collections of higher dimensional continua, Ph. D. Thesis, University of Wisconsin, 1958.
  • 6. B. Knaster, Un continu dont tout sous-continu est indecomposable, Fund. Math. 3(1922), 247-286.
  • 7. W. Lewis, Continuous curves of pseudo-arcs, Houston J. Math. 11(1985), 91-99. MR 86e:54038
  • 8. W. Lewis, The pseudo-arc, Contemporary Math. 117(1991), 103-123. MR 92h:54046
  • 9. W. Lewis and J. J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4(1978), 209-222. MR 58:2750
  • 10. List of the works achieved in the field of mathematics and sciences in Poland during the German occupation, 1939-1945, Polish Academy of Sciences and Letters, Kraków 1947. MR 10:276e
  • 11. 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 10:56i
  • 12. R. L. Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27(1925), 416-428.
  • 13. R. B. Sher, Realizing cell-like maps in Euclidean space, General Topology and its Appl. 2(1972), 75-89. MR 46:2683

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 54F15, 54F50, 54B15

Retrieve articles in all journals with MSC (1991): 54F15, 54F50, 54B15

Additional Information

Janusz R. Prajs
Affiliation: Institute of Mathematics, Opole University, ul. Oleska 48, 45-052 Opole, Poland

Keywords: continuous decomposition, continuum, plane, pseudo-arc
Received by editor(s): May 25, 1994
Received by editor(s) in revised form: February 3, 1998
Published electronically: July 1, 1999
Dedicated: To the memory of Professor Bronisław Knaster
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society