  We introduce the notion of (abelian) similarity scheme, as a constructive
model for topological self-similar fractals, in the same way in which the
notion of iterated function system furnishes a constructive notion of
self-similar fractals in a metric environment. At the same time, our notion
gives a constructive approach to the Kigami-Kameyama notion of topological
fractals, since a similarity scheme produces a topological fractal a la
Kigami-Kameyama, and many Kigami-Kameyama topological fractals may be
constructed via similarity schemes. Our scheme consists of objects
$X_0\stackrel{\varphi}{\rightarrow}X_1\stackrel{\pi}{\leftarrow} Y\times X_0$,
where $X_0,X_1$ and $Y$ are compact Hausdorff spaces, the map $\varphi$ is
continuous injective and the map $\pi$ is continuous surjective. This scheme
produces a sequence $X_n$, $n\in\mathbb{N}$, of compact Hausdorff spaces, $X_n$
embedded in $X_{n+1}$, and a compact Hausdorff space $X_\infty$ giving a sort
of injective limit space, which turns out to be self-similar. We observe that
the space $Y$ parametrizes the generalized similarity maps, and finiteness of
$Y$ is not required.
