Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex