PROBLEMS CONCERNING THIN SYSTEMS

Abstract

In this paper, we introduce and discuss the concept of thin system in the area of uniform albegras. Let X bea compact subset of C and let C(X) be the set of all continuous functions from X into C. Then Ro(X) is the set of restrictions to X of rational functions with poles off X and RX) is the closure of Ro(X) in C(X). We have proved that if X is a compact subset of C with int (X) (the interior of X) is an empty set, then Ro(X) is a dense thin system in R(X). Also, we have proved that if A is a uniform algebra on the maximal ideal space A, and S is a thin system in A, then the smallest subalgebra of A containing S is a thin system in A.