Mappings of the Sierpiński curve onto itself
HTML articles powered by AMS MathViewer
- by J. J. Charatonik PDF
- Proc. Amer. Math. Soc. 92 (1984), 125-132 Request permission
Abstract:
Given two points $p$ and $q$ of the Sierpiński universal plane curve $S$, necessary and/or sufficient conditions are discussed in the paper under which there is a mapping $f$ of $S$ onto itself such that $f(p) = q$ and $f$ belongs to one of the following: homeomorphisms, local homeomorphisms, local homeomorphisms in the large sense, open, simple or monotone mappings.References
- Leonard M. Blumenthal and Karl Menger, Studies in geometry, W. H. Freeman and Co., San Francisco, Calif., 1970. MR 0273492
- Karol Borsuk and R. Molski, On a class of continuous mappings, Fund. Math. 45 (1957), 84–98. MR 102063, DOI 10.4064/fm-45-1-84-98
- B. Knaster and A. Lelek, Coutures et tapis, Fund. Math. 45 (1958), 186–199 (French). MR 102065, DOI 10.4064/fm-45-1-200-212
- J. Krasinkiewicz, On homeomorphisms of the Sierpiński curve, Prace Mat. 12 (1969), 255–257. MR 0247618
- P. Krupski, Continua which are homogeneous with respect to continuity, Houston J. Math. 5 (1979), no. 3, 345–356. MR 559975
- K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
- A. Lelek, Sur l’unicohérence, les homéomorphies locales et les continus irréductibles, Fund. Math. 45 (1957), 51–63 (French). MR 99637, DOI 10.4064/fm-45-1-51-63
- T. Maćkowiak, Local homeomorphisms onto tree-like continua, Colloq. Math. 38 (1977), no. 1, 63–68. MR 464200, DOI 10.4064/cm-38-1-63-68 S. Mazurkiewicz, Sur les continus homogènes, Fund. Math. 5 (1924), 137-146.
- G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320–324. MR 99638, DOI 10.4064/fm-45-1-320-324 —, Analytic topology, Amer. Math. Soc. Colloq. Publ., vol. 28, Amer. Math. Soc., Providence, R.I., 1963.
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 92 (1984), 125-132
- MSC: Primary 54F15; Secondary 54F50
- DOI: https://doi.org/10.1090/S0002-9939-1984-0749904-1
- MathSciNet review: 749904