The diagonal of a first countable paratopological group, submetrizability, and related results

Authors

  • A. V. Arhangelskii Ohio University
  • Angelo Bella University of Catania

DOI:

https://doi.org/10.4995/agt.2007.1881

Keywords:

Gδ-diagonal of rank n, Semitopological and paratopological groups, Souslin number, Submetrizability

Abstract

We discuss some properties stronger than Gδ-diagonal. Among other things, we prove that any first countable paratopological group has a Gδ-diagonal of infinite rank and hence also a regular Gδ-diagonal. This answer a question recently asked by Arhangel’skii and Burke.

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Author Biographies

A. V. Arhangelskii, Ohio University

Department of Mathematics

Angelo Bella, University of Catania

Department of Mathematics

References

A. V. Arhangel'skii and D. Burke, Spaces with regular Gδ-diagonal, Topology Appl. 153, no. 11 (2006), 1917-1929. https://doi.org/10.1016/j.topol.2005.07.013

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A. Bella, More on cellular extent and related cardinal functions, Boll. Un. Mat. Ital. 7, no. 3A (1989), 61-68.

R. Z. Buzyakova, Cardinalities of ccc-spaces with regular Gδ-diagonal, Topology Appl. 153, no. 11 (2006), 1696-1698. https://doi.org/10.1016/j.topol.2005.06.004

R. Engelking, General Topology, 1977.

C. Liu, A note on paratopological groups, Comment. Math. Univ. Carolinae 47, no. 4 (2006), 633-640.

V. Mc Arthur, Gδ-diagonal and metrization theorems, Pacific J. Math. 44 (1973), 213-217. https://doi.org/10.2140/pjm.1973.44.613

V. V. Uspenskii, Large F -discrete spaces having the Souslin property, Comment. Math. Univ. Carolinae 25, no. 2 (1984), 257-260.

P. Zenor, On spaces with regular Gδ-diagonal, Pacific J. Math. 40 (1972), 959-963. https://doi.org/10.2140/pjm.1972.40.759

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How to Cite

[1]
A. V. Arhangelskii and A. Bella, “The diagonal of a first countable paratopological group, submetrizability, and related results”, Appl. Gen. Topol., vol. 8, no. 2, pp. 207–212, Oct. 2007.

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Section

Regular Articles