CONTINUOUSLY REMOVABLE SETS FOR QUASICONFORMAL MAPPINGS


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Abstract

Let D be a domain in the n-dimensional Euclidean space Rn, n ≥ 2, and let E be a compact in D. The paper presents conditions on the compact E under which any homeomorphic mapping f = D \ E → Rn can be extended to a continuous mapping f = D → R = Rn ∪ {∞}. These conditions define the class of NCS-compacts, which, for n = 2, coincides with the class of topologically removable compacts for conformal and quasiconformal mappings. Bibliography: 11 titles.

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