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1996 | 150 | 2 | 113-126
Tytuł artykułu

Exactly two-to-one maps from continua onto arc-continua

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable.
Słowa kluczowe
Rocznik
Tom
150
Numer
2
Strony
113-126
Opis fizyczny
Daty
wydano
1996
otrzymano
1993-11-30
poprawiono
1995-12-01
Twórcy
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
autor
  • Department of Mathematics, Auburn University, Alabama 36849-5310, U.S.A.
  • Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
  • [1] J. M. Aarts, The structure of orbits in dynamical systems, Fund. Math. 129 (1988), 39-58.
  • [2] J. M. Aarts and M. Martens, Flows on one-dimensional spaces, Fund. Math. 131 (1988), 53-67.
  • [3] J. M. Aarts and L. G. Oversteegen, Flowbox manifolds, Trans. Amer. Math. Soc. 327 (1991), 449-463.
  • [4] W. Dębski, Two-to-one maps on solenoids and Knaster continua, Fund. Math. 141 (1992), 277-285.
  • [5] W. Dębski, J. Heath and J. Mioduszewski, Exactly two-to-one maps from continua onto some tree-like continua, Fund. Math., 269-276.
  • [6] W. H. Gottschalk, On k-to-1 transformations, Bull. Amer. Math. Soc. 53 (1947), 168-169.
  • [7] J. Grispolakis and E. D. Tymchatyn, Continua which are images of weakly confluent mappings only, (I), Houston J. Math. 5 (1979), 483-501.
  • [8] O. G. Harrold, Exactly (k,1) transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823-834.
  • [9] J. Heath, 2-to-1 maps with hereditarily indecomposable images, Proc. Amer. Math. Soc. 113 (1991), 839-846.
  • [10] J. Heath, There is no exactly k-to-1 function from any continuum onto [0,1], or any dendrite, with only finitely many discontinuities, Trans. Amer. Math. Soc. 306 (1988), 293-305.
  • [11] J. Hocking and G. Young, Topology, Addison-Wesley, 1961.
  • [12] H. B. Keynes and M. Sears, Modeling expansion in real flows, Pacific J. Math. 85 (1979), 111-124.
  • [13] J. Mioduszewski, On two-to-one continuous functions, Dissertationes Math. (Rozprawy Mat.) 24 (1961).
  • [14] S. B. Nadler, Jr. and L. E. Ward, Jr., Concerning exactly (n,1) images of continua, Proc. Amer. Math. Soc. 87 (1983), 351-354.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv150i2p113bwm
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