Shahrood University of TechnologyJournal of Algebraic Systems2345-51288120200901ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS1726176310.22044/jas.2019.8356.1409ENM. R. Ahmadi ZandDepartment of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran.S. RostamiDepartment of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran.Journal Article20190427Abstract. A topological group H is called ω -narrow if for every<br />neighbourhood V of it’s identity element there exists a countable<br />set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G<br />such that xe(x) = e(x)x = x and for every x ∈ G there exists<br />x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also let G be a topological space and the operation and inversion mapping are continuous,<br />then G is called a topological generalized group. If {e(x) | x ∈ G} is<br />countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrow<br />topological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological<br />generalized groups are introduced and studiedhttps://jas.shahroodut.ac.ir/article_1763_7eca9f8c7119e52f92adbafaae64e02c.pdf