Collective argumentation studies how to reach a collective decision that is acceptable to the group in a debate. I introduce the concept of topological restriction to enrich collective argumentation. Topological restrictions are rational constraints assumed to be satisfied by individual agents. We assume that in a debate, for every pair of arguments that are being considered, every agent indicates whether the first one attacks the second, i.e., an agent’s argumentative stance is characterized as an argumentation framework, and only argumentation frameworks that satisfy topological constraints are allowed. The topological constraints we consider in this paper include acyclicity, symmetry, as well as a newly defined topological property called t-self-defense. We show that when the profile of argumentation frameworks provided by agents satisfies topological restrictions, impossibility results during aggregation can be avoided. Furthermore, if a profile is topological-restricted with respect to t-self-defense, then the majority rule guarantees admissibility during aggregation.