An algebraic approach to data structures is presented
which is somewhat related to the ideas of the Vienna
method. After having introduced and investigated the basic
operations of object space and their algebraic properties,
continuous mappings are considered, thus getting the basis
for solving fixpoint equations. Several interesting substructures
of an object space are looked at: submonoids are
associated whith data types; finite objects (corresponding
to finite trees) as well as rational objects (corresponding
to finite graphs) form subspaces. The rational objects are
uniquely characterized as solutions of rational systems of
equations which are particularly significant for the semantics
of data type declarations.