Summary In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of ℰ T n ${\cal E}_T^n $ and in [20] he has formalized that ℰ T n ${\cal E}_T^n $ is second-countable, we build (in the topological sense defined in [23]) a denumerable base of ℰ T n ${\cal E}_T^n $ . Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝ n [16], semi-intervalle (borné) de ℝ n [22]). We conclude with the definition of Chebyshev distance [11].