Dense Sδ-diagonals and linearly ordered extensions

Abstract

The notion of the Sδ-diagonal was introduced by H. R. Bennett to study the quasi-developability of linearly ordered spaces. In an earlier paper, we obtained a characterization of topological spaces with an Sδ-diagonal and we showed that the Sδ-diagonal property is stronger than the quasi-Gδ-diagonal -diagonal property. In this paper, we define a dense Sδ-diagonal of a space and show that two linearly ordered extensions of a generalized ordered space X have dense Sδ-diagonals if the sets of right and left looking points are countable.

Keywords

• Sδ-diagonal
• Dense Sδ-diagonal
• Linearly ordered space (LOTS)
• Generalized ordered space (GO-space)
• Linearly ordered extension