Continuous decompositions of Peano plane continua into pseudo-arcs

• Autorzy: Janusz R. Prajs
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

continuous decomposition; locally connected continuum; local separating point; open homogeneity; pseudo-arc; 2-manifold

Kategorie tematyczne

• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54F15: Continua and generalizations
• 54F99: None of the above, but in this section
• 54F65: Topological characterizations of particular spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 158
• Numer: 1
• Strony: 23-40

Daty

wydano

1998

otrzymano

1996-12-11

poprawiono

1997-11-18

poprawiono

1998-04-14

Twórcy

autor

Janusz R. Prajs

• 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.