Hyperspaces of hereditarily indecomposable plane continua
HTML articles powered by AMS MathViewer
- by E. D. Tymchatyn
- Proc. Amer. Math. Soc. 56 (1976), 300-302
- DOI: https://doi.org/10.1090/S0002-9939-1976-0405334-9
- PDF | Request permission
Abstract:
In this note we prove that if $X$ is a hereditarily indecomposable plane continuum then the hyperspace $C(X)$ can be embedded in Euclidean $3$-space.References
- E. Dyer and M.-E. Hamstrom, Completely regular mappings, Fund. Math. 45 (1958), 103–118. MR 92959, DOI 10.4064/fm-45-1-103-118
- J. Krasinkiewicz, On the hyperspaces of certain plane continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 23 (1975), no. 9, 981–983 (English, with Russian summary). MR 493999
- William R. R. Transue, On the hyperspace of subcontinua of the pseudoarc, Proc. Amer. Math. Soc. 18 (1967), 1074–1075. MR 222851, DOI 10.1090/S0002-9939-1967-0222851-X H. Whitney, Regular families of curves, Proc. Nat. Acad. Sci. U.S.A. 18 (1932), 275-278.
- Gordon Thomas Whyburn, Analytic Topology, American Mathematical Society Colloquium Publications, Vol. 28, American Mathematical Society, New York, 1942. MR 0007095
- J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22–36. MR 6505, DOI 10.1090/S0002-9947-1942-0006505-8
Bibliographic Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 56 (1976), 300-302
- MSC: Primary 54B20; Secondary 54F50
- DOI: https://doi.org/10.1090/S0002-9939-1976-0405334-9
- MathSciNet review: 0405334