Continuous decompositions of Peano plane continua into pseudo-arcs

Janusz Prajs

Fundamenta Mathematicae (1998)

  • Volume: 158, Issue: 1, page 23-40
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Prajs, Janusz. "Continuous decompositions of Peano plane continua into pseudo-arcs." Fundamenta Mathematicae 158.1 (1998): 23-40. <http://eudml.org/doc/212300>.

@article{Prajs1998,
abstract = {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.},
author = {Prajs, Janusz},
journal = {Fundamenta Mathematicae},
keywords = {continuous decomposition; locally connected continuum; local separating point; open homogeneity; pseudo-arc; 2-manifold},
language = {eng},
number = {1},
pages = {23-40},
title = {Continuous decompositions of Peano plane continua into pseudo-arcs},
url = {http://eudml.org/doc/212300},
volume = {158},
year = {1998},
}

TY - JOUR
AU - Prajs, Janusz
TI - Continuous decompositions of Peano plane continua into pseudo-arcs
JO - Fundamenta Mathematicae
PY - 1998
VL - 158
IS - 1
SP - 23
EP - 40
AB - 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.
LA - eng
KW - continuous decomposition; locally connected continuum; local separating point; open homogeneity; pseudo-arc; 2-manifold
UR - http://eudml.org/doc/212300
ER -

References

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  4. [4] K. Borsuk, On embedding curves into surfaces, Fund. Math. 59 (1966), 73-89. 
  5. [5] M. Brown, Continuous collections of higher dimensional continua, Ph.D. thesis, University of Wisconsin, 1958. 
  6. [6] C J. J. Charatonik, Mappings of the Sierpiński curve onto itself, Proc. Amer. Math. Soc. 92 (1984), 125-132. Zbl0524.54010
  7. [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. 
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  10. [10] M. Levin, Bing maps and finite-dimensional maps, Fund. Math. 151 (1996), 47-52. Zbl0860.54028
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  13. [13] W. Lewis, Observations on the pseudo-arc, Topology Proc. 9 (1984), 329-337. Zbl0577.54038
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  15. [15] W. Lewis, The pseudo-arc, in: Contemp. Math. 117, Amer. Math. Soc. 1991, 103-123. Zbl0736.54027
  16. [16] W. Lewis, Another characterization of the pseudo-arc, Bull. Polish Acad. Sci., to appear. Zbl0945.54028
  17. [17] W. Lewis and J. J. Walsh, A continuous decomposition of the plane into pseudo-arcs, Houston J. Math. 4 (1978), 209-222. Zbl0393.54007
  18. [18] M R. L. Moore, Concerning upper semicontinuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), 416-428. Zbl51.0464.03
  19. [19] S. Mazurkiewicz, Sur les continus homogènes, Fund. Math. 5 (1924), 137-146. 
  20. [20] J. R. Prajs, A continuous circle of pseudo-arcs filling up the annulus, Trans. Amer. Math. Soc., to appear. Zbl0936.54019
  21. [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. [22] C. R. Seaquist, Monotone open homogeneity of the Sierpiński curve, Topology Appl., to appear. Zbl0923.54012
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  24. [24] Y G. S. Young, Characterization of 2-manifolds, Duke Math. J. 14 (1947), 979-990. Zbl0029.23204

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