  We propose a unifying approach to many approximation properties studied in
the literature from the 1930s up to our days. To do so, we say that a Banach
space E has the (I,J,{\tau})-approximation property if E-valued operators
belonging to the operator ideal I can be approximated, with respect to the
topology {\tau}, by operators belonging to the operator ideal J. Restricting
{\tau} to a class of linear topologies, which we call ideal topologies, this
concept recovers many classical/recent approximation properties as particular
instances and several important known results are particular cases of more
general results that are valid in this abstract framework.
