A Property of GO-Topologies on the Reals

Abstract

In 1981 Peter de Caux proved that finite powers of the Sorgenfrey line are hereditarily D-spaces. In this paper we build on de Caux's technique to show that any subspace of a finite power of the reals with a generalized ordered topology is a finite union of D-spaces and therefore a transitively D-space. We also note that finite powers of Sorgenfrey Suslin lines are D-spaces.