Dense Sδ-diagonals and linearly ordered extensions

Masami Hosobuchi


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.


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

Full Text:



A. V. Arhangel'skii and Lj. D. Kocinac, On a dense Gδ-diagonal, Publ. L'Institut Math. 47 (61) (1990), 121-126.

H. R. Bennett, LOTS with Sδ-diagonals, Topology Proc. 12 (1987), 211-216.

H. R. Bennett, M. Hosobuchi and D. J. Lutzer, A note on perfect generalized ordered spaces, Rocky Mountain J. Math. 29 (4) (1999), 1195-1207.

H. R. Bennett and D. J. Lutzer, Point countability in generalized ordered spaces, Topology Appl. 71 (1996), 149-165.

M. Hosobuchi, Sδ-diagonals and generalized ordered spaces, J. Tokyo Kasei Gakuin Univ. (Nat. Sci. Tech.) 41 (2001), 1-7.

D. J. Lutzer, A metrization theorem for linearly orderable spaces, Proc. Amer. Math. Soc. 22 (1969), 557-558.

D. J. Lutzer, On generalized ordered spaces, Dissertationes Math. 89 (1971), 1-32.

T. Miwa and N. Kemoto, Linearly ordered extensions of GO spaces, Topology Appl. 54 (1993), 133-140.

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147