  We present a construction, called the limit of a tree system of spaces (or,
less formally, a tree of spaces). The construction is designed to produce
compact metric spaces that resemble fractals, out of more regular spaces, such
as closed manifolds, compact polyhedra, compact Menger manifolds, etc. Such
spaces are potential candidates to be homeomorphic to ideal boundaries of
infinite groups. A very special case of this construction, trees of manifolds
(known also as Jakobsche spaces), has been studied in the literature. We
present here a different approach, much more general, and, as we believe, much
more convenient for establishing various basic properties of the resulting
spaces, in a more general setting. Already in the case of trees of manifolds,
using this approach we clarify, correct and extend so far known results and
properties.
