ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS

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} is countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ωnarrowtopological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological generalized groups are introduced and studied