About G-topological groups

Key Points

• The aim is to define G-topological groups and explore their properties through examples and generalizations.
• Defined G-topological groups based on a method G
• Provided counter-examples to illustrate G-topological groups
• Extended existing properties of topological groups to the context of G-topological groups.
• Established the uniqueness of limits for convergent sequences in G-topological groups
• Highlighted counter-examples that demonstrate complexities in G-topological groups
• Outlined similarities and differences in properties compared to standard topological groups.