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An uncountable collection of mutually incomparable chainable continua

Author: Marwan M. Awartani
Journal: Proc. Amer. Math. Soc. 118 (1993), 239-245
MSC: Primary 54F15; Secondary 54D35
MathSciNet review: 1092914
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Abstract: We exhibit the existence of continuum many compactifications of the ray with the arc as remainder, no one of which maps onto any other. We also obtain continuum many pathwise connected circularly chainable continua no one of which maps onto any other. The involved constructions and proofs are combinatorial in nature.

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

  • [1] M. M. Awartani, Compactifications of the ray with the arc as remainder, Topology Proc. 9 (1984), 201-215. MR 828980 (87h:54049)
  • [2] -, The fixed remainder property for self homeomorphisms of Elsa continua, Topology Proc. 11 (1986), 225-238. MR 945500 (89g:54073)
  • [3] D. P. Bellamy, An uncountable collection of chainable continua, Trans. Amer. Math. Soc. 160 (1971), 297-304. MR 0286076 (44:3292)
  • [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 semicontinuous continuum valued mappings onto circle-like continua, Fund. Math. 60 (1967), 233-239. Mr 36, 3321. MR 0220255 (36:3321)
  • [6] T. Maćkowiak, The condensation of singularities in arclike continua, Houston J. Math. 11 (1985), 535-558. MR 837992 (87m:54099)
  • [7] -, Singular arclike continua, Dissertations Math. (Rozprawy Mat.) 257 (1986), 1-35.
  • [8] J. W. Rogers, Jr., Continuous mappings on continua, Proc. Auburn Topology Conference, March 1969, pp. 94-97. MR 0385822 (52:6681)
  • [9] -, Pseudo-circles and universal circularly chainable continua, Doctoral dissertation, Univ. of California, Riverside, CA, 1968.

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Keywords: Chainable and circularly chainable continua, compactification, mapping between continua
Article copyright: © Copyright 1993 American Mathematical Society

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