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1994-1995 | 146 | 2 | 159-169
Tytuł artykułu

The disjoint arcs property for homogeneous curves

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The local structure of homogeneous continua (curves) is studied. Components of open subsets of each homogeneous curve which is not a solenoid have the disjoint arcs property. If the curve is aposyndetic, then the components are nonplanar. A new characterization of solenoids is formulated: a continuum is a solenoid if and only if it is homogeneous, contains no terminal nontrivial subcontinua and small subcontinua are not ∞-ods.
Rocznik
Tom
146
Numer
2
Strony
159-169
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-10-05
Twórcy
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland, krupski@math.uni.wroc.pl
Bibliografia
  • [1] R. D. Anderson, One-dimensional continuous curves and a homogeneity theorem, Ann. of Math. 68 (1958), 1-16.
  • [2] M. Bestvina, Characterizing k-dimensional universal Menger compacta, Mem. Amer. Math. Soc. 380 (1988).
  • [3] J. H. Case, Another 1-dimensional homogeneous continuum which contains an arc, Pacific J. Math. 11 (1961), 455-469.
  • [4] E. Duda, P. Krupski and J. T. Rogers, On locally chainable homogeneous continua, Topology Appl. 42 (1991), 95-99.
  • [5] E. G. Effros, Transformation groups and C*-algebras, Ann. of Math. 81 (1965), 38-55.
  • [6] F. B. Jones, The aposyndetic decomposition of homogeneous continua, Topology Proc. 8 (1983), 51-54.
  • [7] J. Krasinkiewicz, On homeomorphisms of the Sierpiński curve, Comment. Math. Prace Mat. 12 (1969), 255-257.
  • [8] P. Krupski, Recent results on homogeneous curves and ANR's, Topology Proc. 16 (1991), 109-118.
  • [9] P. Krupski and J. R. Prajs, Outlet points and homogeneous continua, Trans. Amer. Math. Soc. 318 (1990), 123-141.
  • [10] T. Maćkowiak, Terminal continua and the homogeneity, Fund. Math. 127 (1987), 177-186.
  • [11] T. Maćkowiak and E. D. Tymchatyn, Continuous mappings on continua II, Dissertationes Math. (Rozprawy Mat.) 225 (1984).
  • [12] J. C. Mayer, L. G. Oversteegen and E. D. Tymchatyn, The Menger curve. Characterization and extension of homeomorphisms of non-locally-separating closed subsets, ibid. 252 (1986).
  • [13] P. Minc and J. T. Rogers, Jr., Some new examples of homogeneous curves, Topology Proc. 10 (1985), 347-356.
  • [14] R. L. Moore, Triodic continua in the plane, Fund. Math. 13 (1929), 261-263.
  • [15] J. R. Prajs, Openly homogeneous continua having only arcs for proper subcontinua, Topology Appl. 31 (1989), 133-147.
  • [16] J. T. Rogers, Jr., Decompositions of homogeneous continua, Pacific J. Math. 99 (1982), 137-144.
  • [17] J. T. Rogers, An aposyndetic homogeneous curve that is not locally connected, Houston J. Math. 9 (1983), 433-440.
  • [18] J. T. Rogers, Aposyndetic continua as bundle spaces, Trans. Amer. Math. Soc. 283 (1984), 49-55.
  • [19] J. T. Rogers, Homogeneous curves that contain arcs, Topology Appl. 21 (1985), 95-101.
  • [20] J. T. Rogers, Decompositions of continua over the hyperbolic plane, Trans. Amer. Math. Soc. 310 (1988), 277-291.
  • [21] G. T. Whyburn, Analytic Topology, Amer. Math. Soc. Colloq. Publ. 28, Providence, R.I., 1942.
  • [22] G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320-324.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv146i2p159bwm
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