  In this paper, we construct (a) a pair of two regular Cantor sets in higher
dimension which exhibits $C^1$-stable intersection and (b) a hyperbolic basic
set which exhibits $C^2$-robust homoclinic tangency of the largest codimension
for any higher dimensional manifold, using blenders. The former implies that an
analog of Moreira's theorem on Cantor sets in the real line does not hold in
higher dimension. The latter solves a question posed by Barrientos and
A.Raibekas.
