The disjoint arcs property for homogeneous curves

Paweł Krupski

Fundamenta Mathematicae (1995)

  • Volume: 146, Issue: 2, page 159-169
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Krupski, Paweł. "The disjoint arcs property for homogeneous curves." Fundamenta Mathematicae 146.2 (1995): 159-169. <http://eudml.org/doc/212059>.

@article{Krupski1995,
abstract = {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.},
author = {Krupski, Paweł},
journal = {Fundamenta Mathematicae},
keywords = {homogeneous continuum; aposyndetic curve; solenoid; disjoint arcs property; Menger universal curve; aposyndetic continuum; DAP},
language = {eng},
number = {2},
pages = {159-169},
title = {The disjoint arcs property for homogeneous curves},
url = {http://eudml.org/doc/212059},
volume = {146},
year = {1995},
}

TY - JOUR
AU - Krupski, Paweł
TI - The disjoint arcs property for homogeneous curves
JO - Fundamenta Mathematicae
PY - 1995
VL - 146
IS - 2
SP - 159
EP - 169
AB - 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.
LA - eng
KW - homogeneous continuum; aposyndetic curve; solenoid; disjoint arcs property; Menger universal curve; aposyndetic continuum; DAP
UR - http://eudml.org/doc/212059
ER -

References

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  4. [4] E. Duda, P. Krupski and J. T. Rogers, On locally chainable homogeneous continua, Topology Appl. 42 (1991), 95-99. Zbl0764.54023
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  22. [22] G. T. Whyburn, Topological characterization of the Sierpiński curve, Fund. Math. 45 (1958), 320-324. Zbl0081.16904

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