The character group of a topological group that is an abelian group consists of its continuous group homomorphisms to the circle group, with pointwise multiplication. For a finite group, all characters are continuous and their values are roots of unity, so this agrees with the character group of a finite abelian group.
A character group typically refers to a collection or set of characters that share certain characteristics or properties, often used in various contexts including literature, psychology, gaming, and social dynamics. Here are a few interpretations of the term: 1. **Literature and Media**: In storytelling, a character group can refer to a cast of characters that interact within a narrative. This can include protagonists, antagonists, and supporting characters who may have different roles, motivations, and relationships.
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