Developable spaces and nearness structures

Abstract

Abstract. Necessary and sufficient conditions on a nearness structure are provided for which the underlying topology is developable. It is also shown that a topology is developable if and only if it admits a compatible nearness structure with a countable base. Finally it is shown that a topological space is embeddable in a complete Moore space if and only if it admits a compatible nearness structure satisfying certain stated conditions. Moreover, the complete Moore space is homeomorphic to Herrlich's completion of the space with the specified nearness structure.