摘要：Let (𝑋,𝑑) be a metric space and a sequence of continuous maps 𝑓𝑛∶𝑋→𝑋 that converges uniformly to a map 𝑓. We investigate the transitive subsets of 𝑓𝑛 whether they can be inherited by 𝑓 or not. We give sufficient conditions such that the limit map 𝑓 has a transitive subset. In particular, we show the transitive subsets of 𝑓𝑛 that can be inherited by 𝑓 if 𝑓𝑛 converges uniformly strongly to 𝑓.
