On paratopological groups
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Abstract In this paper, we firstly construct a Hausdorff non-submetrizable paratopological group G in which every point is a G δ -set, which gives a negative answer to Arhangelʼskii and Tkachenkoʼs question [A.V. Arhangelʼskii, M. Tkachenko, Topological Groups and Related Structures, Atlantis Press and World Sci., 2008]. We also prove that each first-countable Abelian paratopological group is submetrizable. Moreover, we discuss developable paratopological groups and construct a non-metrizable, separable, Moore paratopological group. Further, we prove that a regular, countable, locally k ω -paratopological group is a discrete topological group or contains a closed copy of S ω . 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 Arhangelʼskii and Tkachenkoʼs question [A.V. Arhangelʼskii, M. Tkachenko, Topological Groups and Related Structures, Atlantis Press and World Sci., 2008]. Some questions are posed.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f406e50f796f62f28544909821d2ba92ee121c21
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Citations in the corpus
- Each regular paratopological group is completely regular (2014, background): “21 in [14], and also generalizes many results on the submetrizability of paratopological groups (see, [16, §8], [11], [18], [14]).”