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1998 | 158 | 1 | 23-40
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Continuous decompositions of Peano plane continua into pseudo-arcs

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Locally planar Peano continua admitting continuous decomposition into pseudo-arcs (into acyclic curves) are characterized as those with no local separating point. This extends the well-known result of Lewis and Walsh on a continuous decomposition of the plane into pseudo-arcs.
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Bibliografia
  • [1] A R. D. Anderson, On collections of pseudo-arcs, Abstract 337t, Bull. Amer. Math. Soc. 56 (1950), 350.
  • [2] W. Bajguz, Remark on embedding curves in surfaces, preprint.
  • [3] R. H. Bing, Concerning hereditarily indecomposable continua, Pacific J. Math. 1 (1951), 43-51.
  • [4] K. Borsuk, On embedding curves into surfaces, Fund. Math. 59 (1966), 73-89.
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  • [10] M. Levin, Bing maps and finite-dimensional maps, Fund. Math. 151 (1996), 47-52.
  • [11] W. Lewis, Pseudo-arc of pseudo-arcs is unique, Houston J. Math. 10 (1984), 227-234.
  • [12] W. Lewis, Continuous curves of pseudo-arcs, ibid. 11 (1985), 225-236.
  • [13] W. Lewis, Observations on the pseudo-arc, Topology Proc. 9 (1984), 329-337.
  • [14] W. Lewis, Continuous collections of hereditarily indecomposable continua, Topology Appl. 74 (1996), 169-176.
  • [15] W. Lewis, The pseudo-arc, in: Contemp. Math. 117, Amer. Math. Soc. 1991, 103-123.
  • [16] W. Lewis, Another characterization of the pseudo-arc, Bull. Polish Acad. Sci., to appear.
  • [17] W. Lewis and J. J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4 (1978), 209-222.
  • [18] M R. L. Moore, Concerning upper semicontinuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), 416-428.
  • [19] S. Mazurkiewicz, Sur les continus homogènes, Fund. Math. 5 (1924), 137-146.
  • [20] J. R. Prajs, A continuous circle of pseudo-arcs filling up the annulus, Trans. Amer. Math. Soc., to appear.
  • [21] C. R. Seaquist, A continuous decomposition of the Sierpiński curve, in: Continua (Cincinnati, Ohio, 1994), Lecture Notes in Pure and Appl. Math. 170, Marcel Dekker, 1995, 315-342.
  • [22] C. R. Seaquist, Monotone open homogeneity of the Sierpiński curve, Topology Appl., to appear.
  • [23] W G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320-324.
  • [24] Y G. S. Young, Characterization of 2-manifolds, Duke Math. J. 14 (1947), 979-990.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv158i1p23bwm
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