中文摘要：

本文研究了度量空间中连续映射构成半群的拓扑熵.利用Patr?ao[8]的方法,给出了度量空间中两种有限个连续映射构成的半群的拓扑d-熵的定义,比较了两种拓扑d-熵的大小.证明了局部紧致可分度量空间上有限个真映射构成的半群的拓扑d-熵和它的一点紧化空间上对应的拓扑熵相等.上面结果推广了Patr?ao的相应结论.

英文摘要：

In this paper,we study the topological entropy of a semigroup of continuous maps on a metric space.By using Patrao's[8]method,we give two de finitions of topological dentropy of a semigroup generated by finite continuous maps on a metric space,the size of these two d-entropies are compared.We also show that the topological dentropy of the semigroup generated by finite proper maps on a locally compact separable metric space and the topological entropy on its one-point compactification space coincide,which extend the results obtained by Patrao.