We prove that the strong and weak topological contractions for automorphisms of connected lie groups are equivalent . we also get that the connected lie group which admits a topological contractive automorphism must be a nilpotent lie group 证明了连通李群自同构的强拓扑压缩性质与弱拓扑压缩性质等价；存在拓扑压缩自同构的连通李群是幂零的。
