The introduction of abstract argumentation has allowed the study of many exciting characteristics of the argumentation process. Nevertheless, while helpful in many aspects, abstraction diminishes the knowledge representation capabilities available to describe naturally occurring features of argumentative dialogues. One of these elements is the consideration of the topics involved in a discussion. In studying dialogical processes, participants recognize that some topics are closely related to the original issue, while others are more distant to the central subject or simply refer to unrelated matters. Consequently, it is reasonable to study different argumentation semantics that consider the focus of a discussion to evaluate acceptability. In this work, we will introduce the necessary representational elements required to reflect the focus of a discussion, and we will propose an extension of the semantics for \emph{multi-topic abstract argumentation frameworks} acknowledging that every argument has its own \emph{zone of relevance} in the argumentation framework, leading to a concept of a neighborhood of legitimate defenses. Furthermore, other semantic elaborations are defined and discussed around this structure.