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Transactions of the American Mathematical Society

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An uncountable collection of chainable continua


Author: David P. Bellamy
Journal: Trans. Amer. Math. Soc. 160 (1971), 297-304
MSC: Primary 54.55
DOI: https://doi.org/10.1090/S0002-9947-1971-0286076-X
MathSciNet review: 0286076
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Abstract: We demonstrate the existence of an uncountable collection of chainable continua, no member of which can be mapped onto any other member. Path connectedness considerations and techniques involving compactifications play an important role in the construction and argument.


References [Enhancements On Off] (What's this?)

  • [1] J. M. Aarts and P. van Emde Boas, Continua as remainders in compact extensions, Nieuw Arch. Wisk. (3) 15 (1967), 34-37. MR 35 #4885. MR 0214033 (35:4885)
  • [2] D. P. Bellamy, A non-metric indecomposable continuum, Duke Math. J. 38 (1971), 15-20. MR 0271911 (42:6792)
  • [3] -, Topological properties of compactifications of a half-open interval, Ph.D. Thesis, Michigan State University, E. Lansing, Mich., 1968.
  • [4] R. H. Bing, Snake-like continua, Duke Math. J. 18 (1951), 653-663. MR 13, 265. MR 0043450 (13:265a)
  • [5] H. Cook, Upper semi-continuous continuum-valued mappings onto circle-like continua, Fund. Math. 60 (1967), 233-239. MR 36 #3321. MR 0220255 (36:3321)
  • [6] J. B. Fugate, Decomposable chainable continua, Trans. Amer. Math. Soc. 123 (1966), 460-468. MR 33 #4906. MR 0196720 (33:4906)
  • [7] J. W. Rogers, Jr., Pseudo-circles and universal circularly chainable continua, Doctoral Dissertation, University of California, Riverside, Calif., 1968.
  • [8] -, Continuous mappings on continua, Proc. Auburn Topology Conference, March 1969, pp. 94-97. MR 0385822 (52:6681)
  • [9] Z. Waraszkiewicz, Une famille indenombrable de continus plans dont aucun n'est l'image continue d'un autre, Fund. Math. 18 (1932), 118-137.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0286076-X
Keywords: Chainable continuum, mappings on continua, compactification
Article copyright: © Copyright 1971 American Mathematical Society

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