Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

A continuous decomposition of the Menger curve into pseudo-arcs

Author(s): Janusz R. Prajs
Journal: Proc. Amer. Math. Soc. 128 (2000), 2487-2491.
MSC (2000): Primary 54F15, 54F50
Posted: February 25, 2000
MathSciNet review: 1707009
Retrieve article in: PDF
This article is available free of charge

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:

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

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:

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: 10.1090/S0002-9939-00-05615-X
PII: S 0002-9939(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
Posted: February 25, 2000
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|