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

A. V. Arhangelskii

United States

Ohio University

Department of Mathematics

Angelo Bella

Italy

University of Catania

Department of Mathematics

Submitted: 2013-11-15

|

Accepted: 2013-11-15

|
DOI: https://doi.org/10.4995/agt.2007.1881
Funding Data

Downloads

Keywords:

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

Supporting agencies:

This research was not funded

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.

Show more Show less

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

A. V. Arhangel'skii and R. Buzyakova, The rank of the diagonal and submetrizability, Comment. Math. Univ. Carolinae 47, no. 4 (2006), 585-597.

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

Show more Show less