Topological characterizations of ordered groups with quasi-divisor theory

For an order embedding G -->(h) Gamma of a partly ordered group G into an l-group F a topology T (W) over cap is introduced on Gamma which is defined by a family of valuations W on G. Some density properties of sets h(G), h(X-t) and (h(X-t) \ { h(g(1)),..., h(g(n))}) (X-t being t-ideals in G) in the topological space (Gamma, T (W) over cap) are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.