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Tytuł artykułu
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Abstrakty
It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated by S. Nadler Jr. and L. E. Ward Jr. (1983), is still neither confirmed nor rejected.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
269-276
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-11-26
poprawiono
1992-05-19
Twórcy
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
autor
- Mathematics Department, Parker Hall, Auburn University, Alabama 36849-5310, U.S.A.
autor
- Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Bibliografia
- [1] D. Fox, k-to-1 continuous transformations, Dissertation, Univ. of California at Riverside, 1973.
- [2] W. H. Gottschalk, On k-to-1 transformations, Bull. Amer. Math. Soc. 53 (1947), 168-169.
- [3] J. Grispolakis and E. D. Tymchatyn, Continua which are images of weakly confluent mappings only (I), Houston J. Math. 5 (1979), 483-501.
- [4] J. Heath, Tree-like continua and exactly k-to-1 functions, Proc. Amer. Math. Soc. 105 (1989), 765-772.
- [5] J. Heath, 2-to-1 maps with hereditarily indecomposable images, ibid. 113 (1991), 839-846.
- [6] W. T. Ingram, An atriodic tree-like continuum with positive span, Fund. Math. 77 (1972), 99-107.
- [7] T. Maćkowiak, Semiconfluent mappings and their invariants, ibid. 79 (1973), 251-264.
- [8] 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
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bwmeta1.element.bwnjournal-article-fmv141i3p269bwm