Dense Sδ-diagonals and linearly ordered extensions
DOI:
https://doi.org/10.4995/agt.2003.2010Keywords:
Sδ-diagonal, Dense Sδ-diagonal, Linearly ordered space (LOTS), Generalized ordered space (GO-space), Linearly ordered extensionAbstract
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.
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