G-topological groups extend first countable topological groups, highlighting unique limits and providing counter-examples.
In this paper, we define a G-topological group on a group endowed with a method G, which generalises the notion of first countable topological groups in which any convergent sequence has a unique limit, give some counter-examples of G-topological groups and then extend the usual properties of topological groups to G-topological groups in this sense.
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Osman Mucuk (2025) studied this question.
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