On paratopological groups
Fucai Lin, Chuan Liu

TL;DR
This paper explores various properties of paratopological groups, constructing examples and proving theorems that clarify conditions for submetrizability, developability, and H-closedness, thereby answering longstanding questions in the field.
Contribution
It provides new examples of non-submetrizable and non-metrizable paratopological groups, and establishes key conditions under which these groups exhibit certain topological properties.
Findings
Constructed a non-submetrizable Hausdorff paratopological group where every point is a G_delta-set.
Proved that first-countable Abelian paratopological groups are submetrizable.
Showed the Sorgenfrey line is not H-closed, answering a question by Arhangel'skind Tkachenko.
Abstract
In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group in which every point is a -set, which gives a negative answer to Arhangel'ski\v{\i}\ and Tkachenko's question [Topological Groups and Related Structures, Atlantis Press and World Sci., 2008]. We prove that each first-countable Abelian paratopological group is submetrizable. Moreover, we discuss developable paratopological groups and construct a non-metrizable, Moore paratopological group. Further, we prove that a regular, countable, locally -paratopological group is a discrete topological group or contains a closed copy of . Finally, we discuss some properties on non-H-closed paratopological groups, and show that Sorgenfrey line is not H-closed, which gives a negative answer to Arhangel'ski\v{\i}\ and Tkachenko's question [Topological Groups and Related…
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras
