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 extend F from K to X, with keeping the contnuous continuous and the Hausdoff Hausdorff dimension of the gragh.
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Can we extand extend a continuos continuous function with keeping Hausdoff Hausdorff dimension? |
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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.
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