On best rational approximation of analytic functions

This paper contains some theorems related to the best approximation ρn(f;E) to a function f in the uniform metric on a compact set E⊂C¯ by rational functions of degree at most n. We obtain results characterizing the relationship between ρn(f;K) and ρn(f;E) in the case when complements of compact sets K and E are connected, K is a subset of the interior Ω of E, and f is analytic in Ω and continuous on E.