Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the monoid of cofinite partial isometries of $\mathbb{N}$ with a
  bounded finite noise   In the paper we study algebraic properties of the monoid
$\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ of cofinite partial
isometries of the set of positive integers $\mathbb{N}$ with the bounded finite
noise $j$. For the monoids $\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$
we prove counterparts of some classical results of Eberhart and Selden
describing the closure of the bicyclic semigroup in a locally compact
topological inverse semigroup. In particular we show that for any positive
integer $j$ every Hausdorff shift-continuous topology $\tau$ on
$\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ is discrete and if
$\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ is a proper dense
subsemigroup of a Hausdorff semitopological semigroup $S$, then $S\setminus
\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ is a closed ideal of $S$,
and moreover if $S$ is a topological inverse semigroup then $S\setminus
\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ is a topological group. Also
we describe the algebraic and topological structure of the closure of the
monoid $\mathbf{I}\mathbb{N}_{\infty}^{\boldsymbol{g}[j]}$ in a locally compact
topological inverse semigroup.

30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol