Perfect sets of finite class without the extension property

A. Goncharov

ArticleOriginal scientific text

Title

Perfect sets of finite class without the extension property

Authors ^1,²

Affiliations

Department of Mathematics, Bilkent University, 06533 Ankara, Turkey
Department of Mathematics, Civil Engineering University, Rostov-na-Donu, Russia

Abstract

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.

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Title

Perfect sets of finite class without the extension property

Affiliations

Abstract

Bibliography