  Let $A(K)$ be the algebra of continuous functions on a compact set
$K\subset\mathbb C$ which are analytic on the interior of $K$, and $R(K)$ the
closure (with the uniform convergence on $K$) of the functions that are
analytic on a neighborhood of $K$. A counterexample of a question made by A.
O'Farrell about the equality of the algebras $R(K)$ and $A(K)$ when
$K=(K_{1}\times[0,1])\cup([0,1]\times K_{2})\subseteq\mathbb C$, with $K_{1}$
and $K_{2}$ compact subsets of $[0,1]$, is given. Also, the equality is proved
with the assumption that $K_{1}$ has no interior.
