A universal hereditarily indecomposable continuum
HTML articles powered by AMS MathViewer
- by Tadeusz Maćkowiak
- Proc. Amer. Math. Soc. 94 (1985), 167-172
- DOI: https://doi.org/10.1090/S0002-9939-1985-0781076-0
- PDF | Request permission
Abstract:
It is proved that there exists a hereditarily indecomposable metric continuum $X$ containing a homeomorphic copy of every hereditarily indecomposable metric continuum. This is a solution of a problem (Problem 125 by H. Cook in University of Houston Problems Book) recalled in $[4,\S 21]$. A similar result was announced by P. Mine.References
- Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
- Józef Krasinkiewicz and Piotr Minc, Mappings onto indecomposable continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 7, 675–680 (English, with Russian summary). MR 464184 T. Maćkowiak, The condensation of singularities in arc-like continua (to appear).
- T. Maćkowiak and E. D. Tymchatyn, Continuous mappings on continua. II, Dissertationes Math. (Rozprawy Mat.) 225 (1984), 57. MR 739739
- Sibe Mardešić and Jack Segal, $\varepsilon$-mappings onto polyhedra, Trans. Amer. Math. Soc. 109 (1963), 146–164. MR 158367, DOI 10.1090/S0002-9947-1963-0158367-X
- Michael C. McCord, Universal, ${\cal P}$-like compacta, Michigan Math. J. 13 (1966), 71–85. MR 188986
Bibliographic Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 167-172
- MSC: Primary 54F20; Secondary 54B25, 54F15, 54F45
- DOI: https://doi.org/10.1090/S0002-9939-1985-0781076-0
- MathSciNet review: 781076