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ArticleOriginal scientific text

Title

The disjoint arcs property for homogeneous curves

Authors 1

Affiliations

  1. Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

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.

Keywords

ENG
homogeneous continuum, aposyndetic curve, solenoid, disjoint arcs property, Menger universal curve

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm146/fm14626.pdf

Fundamenta Mathematicae
1994-1995/146/2
Export to PBN, Opens in new tab
Pages:
159-169
Main language of publication
English
Received
1993-10-05
Published
1995
Exact and natural sciences