  In 2013 Balka and M\'ath\'e showed that in uncountable polish spaces the
typical compact set is not a fractal of any IFS. In 2008 Miculescu and Mihail
introduced a concept of a generalized iterated function system (GIFS in short),
a particular extension of classical IFS, in which they considered families of
mappings defined on finite Cartesian product $X^m$ with values in $X$.
Recently, Secelean extended these considerations to mappings defined on the
space $\ell_\infty(X)$ of all bounded sequences of elements of $X$ endowed with
supremum metric. In the paper we show that in Euclidean spaces a typical
compact set is an attractor in sense of Secelean and that in general in the
polish spaces it can be perceived as selfsimilar in such sense.
