Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $G$-compactness for topological groups with operations   It is well known that for a Hausdorff topological group $X$, the limits of
convergent sequences in $X$ define a function denoted by $\lim$ from the set of
all convergent sequences in $X$ to $X$. This notion has been modified by Connor
and Grosse-Erdmann for real functions by replacing $\lim$ with an arbitrary
linear functional $G$ defined on a linear subspace of the vector space of all
real sequences. Recently some authors have extended the concept to the
topological group setting and introduced the concepts of $G$-continuity,
$G$-compactness and $G$-connectedness. In this paper we prove some results on
different types of $G$-compactness for topological group with operations which
include topological groups, topological rings without identity, R-modules, Lie
algebras, Jordan algebras, and many others.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph