Global \(L\)-neighborhood groups (Q834498)

\(L\)-topological groups (groups equipped with an \(L\)-topology, studied in [ibid. 156, No. 1, 43--54 (2005; Zbl 1081.22001)] are generalized to global \(L\)-neighborhood groups (groups equipped with a global neighborhood structure in the sense of [\textit{W. Gähler}, the author, \textit{A. Kandil} and \textit{A. Nouh} [ibid. 97, No. 2, 225--254 (1998; Zbl 0934.54004)]; it is shown that the category of global \(L\)-neighborhood groups is a topological category over the category of groups, the initial and final global \(L\)-neighborhood groups in this category are characterized.