Let A be a uniform algebra on a
compact Hausdorff space X and let E ⊂ X be a closed subset which is a Gδ.
Denote by BE all functions on X∖E which are uniform limits on compact
subsets of X∖E of bounded sequences from A. It is proved that a relatively
closed subset S of X∖E is an interpolation set and an intersection of peak
sets for BE if and only if each compact subset of S has the same property
w.r.t. A. In some special cases the interpolation sets for BE are characterized in
a similar way. A method for constructing infinite interpolation sets for A
and BE whenever x ∈ E is a peak point for A in the closure of X∖{x}, is
presented.
