关于连续映射半群拓扑熵的一点注记
A REMARK ON THE TOPOLOGICAL ENTROPY OF A SEMIGROUP OF CONTINUOUS MAPS

本文研究了度量空间中连续映射构成半群的拓扑熵.利用Patráo[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Patráo的相应结论.
In this paper, we study the topological entropy of a semigroup of continuous maps on a metric space. By using Patráo[8] method, we give two deflnitions of topological d -entropy of a semigroup generated by flnite continuous maps on a metric space, the size of these two d-entropies are compared. We also show that the topological d-entropy of the semigroup generated by flnite proper maps on a locally compact separable metric space and the topological entropy on its one-point compactiflcation space coincide, which extend the results obtained by Patráo