Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance,  show that such a remainder is Hurewicz if and only it is $$\sigma $$ź-compact. Also, the existence of a Scheepers non-$$\sigma $$ź-compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC.  also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel'skii.
['Angelo Bella', 'Seçil Tokgöz', 'Lyubomyr Zdomskyy']
I am writing a research paper on a idea Menger remainders of topological groups
[{"from": "human", "value": "I am writing a research paper on a idea Menger remainders of topological groups"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:   discuss what kind of constrains combinatorial covering properties of Menger, Scheepers, and Hurewicz impose on remainders of topological groups. For instance,  show that such a remainder is Hurewicz if and only it is $$\\sigma $$\u017a-compact. Also, the existence of a Scheepers non-$$\\sigma $$\u017a-compact remainder of a topological group follows from CH and yields a P-point, and hence is independent of ZFC.  also make an attempt to prove a dichotomy for the Menger property of remainders of topological groups in the style of Arhangel'skii."}]