摘要
研究一致空间上连续变换的拓扑熵的性质和紧一致空间上扩张同胚拓扑熵的计算问题 证明Bowen给出的度量空间的连续变换的拓扑熵由其度量诱导的一致结构决定 ;对于可一致化的紧拓扑空间上的连续变换Adler、Konheim、McAndrew及Bowen定义的拓扑熵相同 ;变换是扩张变换等价于其有生成子 ;
The properties of the topological entropies of continuous transformations in uniform spaces and the calculating problem of the topological entropies of expansive homeomorphisms in compact uniform spaces is considered.It is shown that,(i)The Bowen's topological entropy(TE) defined for uniformly continuous transformations in metric space is decided by the unform structure induced by the metric ;(ii)All TEs defined by Adler,Konheim, and McAndrew & Bowen ,for continuous maps in uniformizable compact space coincide with each other;(iii)A map is expansive homeomorphism if and only if it has a generator; (iv)The TE of an expansive homeomorphism in compact uniform space is decided by its generator or expansive constant. [
出处
《暨南大学学报（自然科学与医学版）》
CAS
CSCD
2000年第3期21-28,共8页
Journal of Jinan University(Natural Science & Medicine Edition)
基金
国务院侨办重点学科基金 !(93A10 9)
关键词
一致空间
连续变换
拓扑熵
扩张变换
生成子
uniform space
continuous transformation
topological entropy
expansive homeomorphism
generator
