The Vietoris topology on rectifiable spaces

A topological space G is said to be a rectifiable space provided that there are a surjective homeomorphism φ:G×G→G×G and an element e∈G such that π ₁°φ=π ₁ and for every x∈G we have φ(x,x)=(x,e), where π ₁:G×G→G is the projection to the first coordinate. Let G be a rectifiable space and C(G) be the family of all non-empty compact subsets of G. In this paper, we study the Vietoris topology on C(G), and show that if G is a locally compact rectifiable space, then (C(G),?) together with the Vietoris topology is a topological semi-right loop.