A continuous decomposition of the Menger curve into pseudo-arcs

Prajs, Janusz

doi:10.1090/S0002-9939-00-05615-X

A continuous decomposition of the Menger curve into pseudo-arcs
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by Janusz R. Prajs PDF

Proc. Amer. Math. Soc. 128 (2000), 2487-2491 Request permission

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

Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. (2) 68 (1958), 1–16. MR 96181, DOI 10.2307/1970040
Robert J. Daverman, Decompositions of manifolds, Pure and Applied Mathematics, vol. 124, Academic Press, Inc., Orlando, FL, 1986. MR 872468
Wayne Lewis and John J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4 (1978), no. 2, 209–222. MR 482693
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.
J. R. Prajs, Continuous decompositions of Peano plane continua into pseudo-arcs, Fund. Math. 158 (1998), 23-40.
Richard B. Sher, Realizing cell-like maps in Euclidean space, General Topology and Appl. 2 (1972), 75–89. MR 303546, DOI 10.1016/0016-660X(72)90039-6
David C. Wilson, Open mappings of the universal curve onto continuous curves, Trans. Amer. Math. Soc. 168 (1972), 497–515. MR 298630, DOI 10.1090/S0002-9947-1972-0298630-0