Glasnik Matematicki, Vol. 41, No.1 (2006), 165-176.

ON LINKING OF CANTOR SETS

Matjaž Željko

Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
e-mail: matjaz.zeljko@fmf.uni-lj.si

Abstract.   We introduce a property L for a subset of a manifold which enables us to pass the geometric linking property from the manifold to this subset. We prove that cubes with handles M and N are linked if and only if subsets X subset Int M and Y subset Int N having property L are linked. We present a criterion which shows that many known Cantor sets explicitly given by defining sequences have this property. As an application of the property L we extend the theorem on rigid Cantor sets thus allowing slightly more complicated terms in their defining sequences.

2000 Mathematics Subject Classification.   57M30.

Key words and phrases.   Geometric linking, Cantor set, defining sequence, rigid Cantor set.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.1.14

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