The diagonal of a first countable paratopological group, submetrizability, and related results
DOI:
https://doi.org/10.4995/agt.2007.1881Keywords:
Gδ-diagonal of rank n, Semitopological and paratopological groups, Souslin number, SubmetrizabilityAbstract
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.
Downloads
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
Downloads
How to Cite
Issue
Section
License
This journal is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike- 4.0 International License.