  In this article we prove the topological minimality of unions of several
almost orthogonal planes of arbitrary dimensions. A particular case was proved
in arXiv:1103.1468, where we proved the Almgren minimality (which is a weaker
property than the topological minimality) of the union of two almost orthogonal
2 dimensional planes. On the one hand, the topological minimality is always
proved by variations of calibration methods, but in this article, we give a
continuous family topological minimal sets, hence calibrations cannot apply.
The advantage of a set being topological minimal (compared to Almgren minimal)
is that its product with $\R^n$ stays topological minimal. This leads also to
finding minimal sets which are unions of non transversal (hence far from almost
orthogonal) planes; On the other hand, regularity for higher dimensional
minimal sets is much less clear than those of dimension 2, hence more efforts
are needed for higher dimensional cases.
