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