%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