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