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Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
23-40
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-12-11
poprawiono
1997-11-18
poprawiono
1998-04-14
Twórcy
autor
- Institute of Mathematics, Opole University, Oleska 48, 45-052 Opole, Poland
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.
- [5] M. Brown, Continuous collections of higher dimensional continua, Ph.D. thesis, University of Wisconsin, 1958.
- [6] C J. J. Charatonik, Mappings of the Sierpiński curve onto itself, Proc. Amer. Math. Soc. 92 (1984), 125-132.
- [7] C J. J. Charatonik, Generalized homogeneity of the Sierpiński universal plane curve, in: Topology. Theory and Applications (Eger, 1983), Colloq. Math. Soc. János Bolyai 41, North-Holland, 1985, 153-158.
- [8] B. Knaster, Un continu dont tout sous-continu est indécomposable, Fund. Math. 3 (1922), 247-286.
- [9] J. Krasinkiewicz, On mappings with hereditarily indecomposable fibers, Bull. Polish Acad. Sci. Math. 44 (1996), 147-156.
- [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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