  In this article we introduce a definition of topological minimal sets, which
is a generalization of that of Mumford-Shah-minimal sets. We prove some general
properties as well as two existence theorems for topological minimal sets. As
an application we prove the topological minimality of the union of two almost
orthogonal planes in $\R^4$, and use it to improve the angle criterion under
which the union of several higher dimensional planes is Almgren-minimal.
