A new approach in index theory

In this paper, we define an analytical index for a continuous family of Fredholm operators parameterized by a topological space $\mathbb{X}$ into a Hilbert space $H,$ as a sequence of integers, extending naturally the usual definition of the index and we prove the homotopy invariance of the index. We give also an extension of the Weyl theorem for normal continuous families and we prove that if $H$ is separable, then the space of B-Fredholm operators on $H$ is path connected.