Search results for "relatively connected sets"

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Quasisymmetric extension on the real line

2018

We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to\mathbb{R}^N$ for some $N\geq n$.

Mathematics::Combinatoricsrelatively connected setsApplied MathematicsGeneral Mathematics010102 general mathematicsta111Extension (predicate logic)Characterization (mathematics)01 natural sciencesCombinatoricsfunktioteoria0103 physical sciencesMathematics::Metric GeometryEmbedding010307 mathematical physics0101 mathematicsReal linequasisymmetric extensionMathematicsProceedings of the American Mathematical Society
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Quasisymmetric extension on the real line

2015

We give a geometric characterization of the sets $E\subset \mathbb{R}$ that satisfy the following property: every quasisymmetric embedding $f: E \to \mathbb{R}^n$ extends to a quasisymmetric embedding $f:\mathbb{R}\to\mathbb{R}^N$ for some $N\geq n$.

funktioteoriarelatively connected setsMathematics::CombinatoricsMathematics - Metric GeometryFOS: MathematicsMathematics::Metric GeometryMetric Geometry (math.MG)quasisymmetric extension30C65
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