Topological characterizations of ordered groups with quasi-divisor theory

Abstract

For an order embedding \(G\mathop \to \limits^h \;\Gamma \) of a partly ordered group G into an l-group Γ a topology ’ is introduced on Γ which is defined by a family of valuations W on G. Some density properties of sets h(G), h(Xt) and \((h(X_t )\backslash \{ h(g_1 ),\;.\;.\;.\;,h(g_n )\} )\) (Xt being t-ideals in G) in the topological space ’ are then investigated, each of them being equivalent to the statement that h is a strong theory of quasi-divisors.