Аннотация:It is shown that, under a natural constraint, a set of generalized rational fractions in an atomless L_1-space is a Chebyshev set with continuous metric projection only if this set is convex. Hence this set is not a uniqueness set in L_1, and therefore, some x∈L_1 has at least two nearest points in this set. As a result, it is shown that the set of classical algebraic fractions Rn,m (consisting of ratios of algebraic polynomials of degree ≤n, ≤m, respectively) is not a Chebyshev set in L_1[a,b], and therefore, there exists a function x∈L_1[a,b] with at least two nearest points in Rn,m. This result solves one long-standing problem in rational approximation.