Another Note on Polynomial vs Rational Approximation Original Research Article

LetEbe a subspace ofC(X) and letR(E)=g/h : g, h∈E; h>0}. We make a simple, yet intriguing observation: if zero is a best approximation toffromE, then zero is a best approximation toffromR(E). We also prove that if {En} is dense inC(X) then for almost allf(in the sense of category)[formula]That extends the results of P. Borwein and S. Zhou who proved it for the case whenEnis the space of algebraic or trigonometric polynomials of degreen.