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Transactions of the American Mathematical Society

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Homogeneous continua in Euclidean $ (n+1)$-space which contain an $ n$-cube are locally connected

Author: Janusz R. Prajs
Journal: Trans. Amer. Math. Soc. 307 (1988), 383-394
MSC: Primary 54F25; Secondary 54C25, 57N35
MathSciNet review: 936823
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Abstract: We prove that each homogeneous continuum which topologically contains an $ n$-dimensional unit cube and lies in $ (n + 1)$-dimensional Euclidean space is locally connected.

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  • [1] R. H. Bing, A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Canad. J. Math. 12 (1960), 209-230. MR 0111001 (22:1869)
  • [2] M. J. Greenberg and J. R. Harper, Algebraic topology, a first course, Benjamin/Cummings, Reading, Mass., 1981. MR 643101 (83b:55001)
  • [3] C. L. Hagopian, Homogeneous plane continua, Houston J. Math. 1 (1975), 35-41. MR 0383369 (52:4250)
  • [4] K. Kuratowski, Topology. II, PWN, Warszawa, 1968.
  • [5] A. Lelek, On the Moore triodic theorem, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 271-276. MR 0148023 (26:5533)
  • [6] T. Maćkowiak and E. D. Tymchatyn, Continuous mappings on continua. II, Dissertationes Math. 225 (1984), 1-57. MR 739739 (87a:54048)
  • [7] S. Mazurkiewicz, Sur les continus homogenes, Fund. Math. 5 (1924), 137-146.

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Keywords: Continuum, embedding, Euclidean space, homogeneity, local connectedness
Article copyright: © Copyright 1988 American Mathematical Society

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