%0 Journal Article %T ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS %J Journal of Algebraic Systems %I Shahrood University of Technology %Z 2345-5128 %A Ahmadi Zand, M. R. %A Rostami, S. %D 2020 %\ 09/01/2020 %V 8 %N 1 %P 17-26 %! ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS %K ω-narrow topological generalized group %K Resolvable topological generalizad group %K Precompact topological generalized group %K Invariance number %R 10.22044/jas.2019.8356.1409 %X Abstract. A topological group H is called ω -narrow if for everyneighbourhood V of it’s identity element there exists a countableset 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) ∈ Gsuch that xe(x) = e(x)x = x and for every x ∈ G there existsx − 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,then G is called a topological generalized group. If {e(x) | x ∈ G} iscountable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrowtopological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topologicalgeneralized groups are introduced and studied %U https://jas.shahroodut.ac.ir/article_1763_7eca9f8c7119e52f92adbafaae64e02c.pdf