Another note on polynomial vs rational approximation (Q1915584)

Borwein and Zhou proved that if zero is a best approximation to \(f\) from the space \(E\) of polynomials of degree \(n\), then zero is also a best approximation to \(f\) from the space of rational functions \(R(E)= \{f/g\); \(f\in E\), \(g\in E\}\). The author extends this result to some subspace \(E\) of the space of real values continuous functions.