##  [Kolmogorov N-Width](/kolmogorov-n-width) 

  ##  [Kolmogorov N-Width](https://mathlogic.quantumdictionary.io/kolmogorov-n-width-0) 

  

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Definition

For a compact set F in a normed linear space and integer n, the Kolmogorov n-width is the smallest possible worst-case approximation error when elements of F are projected onto any n-dimensional linear subspace; formally, d_n(F)=inf_{subspace V, dim V=n} sup_{f in F} dist(f,V).