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A continuous decomposition
of the Menger curve into pseudo-arcs


Author: Janusz R. Prajs
Journal: Proc. Amer. Math. Soc. 128 (2000), 2487-2491
MSC (2000): Primary 54F15, 54F50
DOI: https://doi.org/10.1090/S0002-9939-00-05615-X
Published electronically: February 25, 2000
MathSciNet review: 1707009
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that the Menger universal curve $\mathcal{M}$ admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to $\mathcal{M}$.


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

  • 1. R. D. Anderson, Open mappings of compact continua, Proc. Natl. Acad. Sci., U. S. A. 42(1956), 347-349. MR 17:1230h
  • 2. R. D. Anderson, One-dimensional continuous curves and homogeneity theorem, Ann. of Math. 68(1958), 1-16. MR 20:2676
  • 3. R. J. Daverman, Decompositions of manifolds, Academic Press, Inc. 1986. MR 88a:57001
  • 4. 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
  • 5. R. L. Moore, Concerning triods in the plane and the junction of points of plane continua, Proc. Natl. Acad. Sci., U. S. A. 14(1928), 85-88.
  • 6. J. R. Prajs, Continuous decompositions of Peano plane continua into pseudo-arcs, Fund. Math. 158 (1998), 23-40. CMP 99:01
  • 7. R. B. Sher, Realizing cell-like maps in euclidean space, Gen. Top. and Its Appl. 2 (1972), 75-89. MR 46:2683
  • 8. D. C. Wilson, Open mappings of the universal curve onto continuous curves, Trans. Amer. Math. Soc. 168 (1972), 497-515. MR 45:7682

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Additional Information

Janusz R. Prajs
Affiliation: Institute of Mathematics, Opole University, ul. Oleska 48, 45-052 Opole, Poland
Address at time of publication: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042
Email: jrprajs@math.uni.opole.pl, prajs@math.ttu.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05615-X
Keywords: Continuous decomposition, local separating point, Menger curve, pseudo-arc, quotient space
Received by editor(s): July 2, 1997
Received by editor(s) in revised form: September 11, 1998
Published electronically: February 25, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society

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