Geodesic
Perfect sets of finite class without the extension property
Studia Mathematica, Tome 126 (1997) no. 2, pp. 161-170

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DOI

We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory. 
A. Goncharov. Perfect sets of finite class without the extension property. Studia Mathematica, Tome 126 (1997) no. 2, pp. 161-170. doi: 10.4064/sm-126-2-161-170
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