Connectedness of Ordered Rings of Fractions of C(X) with the m-Topology

Abstract

Abstract. An order is presented on the rings of fractions S^-1C(X)
of C(X), where S is a multiplicatively closed subset of C(X), the
ring of all continuous real-valued functions on a Tychonoff space X. Using this, a topology is defined on S^-1C(X) and for a family of particular multiplicatively closed subsets of C(X) namely m.c. z-subsets, it is shown that S^-1C(X) endowed with this topology is a Hausdorff topological ring. Finally, the connectedness of S^-1C(X) via topological properties of X is investigated.