operator algebra on a Hilbert space. The duality between ordinary spaces $M$ and proper commutative algebras is expressed by the Gel’fand-Naimark theorem which states the fact that the algebra of all continuous functions on $M$ is the only possible type of commutative $C^*$-algebra. Additionally, given a commutative $C^*$-algebra $C$, it is possible to reconstruct a Hausdorff topological space $M$ in order to obtain that $C$ is the algebra of continuous functions on $M$. The study of commutative $C^*$-algebras is equivalent to the study of topological Hausdorff spaces. The previous duality has inspired the identification, in non-commutative geometry, of some algebraical objects as a category of non-commutative topological spaces. Alain Connes [@Connes], one of the founders of non-commutative geometry, has proposed a candidate for the objects of such category, the spectral triples $(\mathcal{A},\mathcal{H}, \mathcal{D})$ [@Connes-1], composed by an algebra $\mathcal{A}$, an Hilbert space $\mathcal{H}$ on which $\mathcal{A}$ is represented and an selfadjoint operator $\mathcal{D}$. In fact, every compact oriented Riemannian manifold can be used to define a spectral triple, this kind of manifold $M$ characterizes a Dirac operator on self-adjoint Clifford module bundles over $M$. Connes, after a conjecture in 1996 [@Connes3] and some considerable attempts of Rennie and Varilly [@Rennie-vari], 