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luka
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Can we extandextend a continuoscontinuous function with keeping HausdoffHausdorff dimension?

Let X be a compact subset of R^d, and K be a compact subset of X, such that Dim_H(X)=Dim_H(K). Let F be a continuous function on K, Can we extandextend F from K to X, with keeping the contnuouscontinuous and the HausdoffHausdorff dimension of the gragh.

Can we extand a continuos function with keeping Hausdoff dimension?

Let X be a compact subset of R^d, and K be a compact subset of X, such that Dim_H(X)=Dim_H(K). Let F be a continuous function on K, Can we extand F from K to X, with keeping the contnuous and the Hausdoff dimension of the gragh.

Can we extend a continuous function with keeping Hausdorff dimension?

Let X be a compact subset of R^d, and K be a compact subset of X, such that Dim_H(X)=Dim_H(K). Let F be a continuous function on K, Can we extend F from K to X, with keeping the continuous and the Hausdorff dimension of the gragh.

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luka
luka
  • 43
  • 1
  • 4

Can we extand a continuos function with keeping Hausdoff dimension?

Let X be a compact subset of R^d, and K be a compact subset of X, such that Dim_H(X)=Dim_H(K). Let F be a continuous function on K, Can we extand F from K to X, with keeping the contnuous and the Hausdoff dimension of the gragh.