拓扑空间上连续自映射的拓扑熵的不变性  

The invariance of topological entropies of continuous self-mappings on topological spaces

作　　者：来阿龙[1] 赵虎[1] 李生刚[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《陕西师范大学学报（自然科学版）》2012年第4期11-15,共5页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071151);陕西省自然科学基金资助项目(2010JM1005);陕西师范大学研究生培养创新基金资助项目(2012CXS038)

摘　　要：研究了拓扑空间上连续自映射的拓扑熵在空间变小或拓扑变弱时是否不变的问题.运用开覆盖、不变子集和非游荡集的理论讨论了拓扑空间上连续自映射的拓扑熵的相关性质.利用这些性质证明了:若拓扑空间上的连续自映射f的非游荡集是紧集,则f的拓扑熵等于f在它的非游荡集上的限制映射的拓扑熵;一个强θ-紧Hausdorff空间(X,T)上的连续自映射的拓扑熵等于这一映射在(X,θ(T))上的拓扑熵,这里θ(T)表示(X,T)中的θ-开集的全体.The problem whether the topological entropy of a continuous self-mapping on a topological space is invariant when the space becomes smaller or its topology becomes weaker is studied. Relevant properties of the topological entropy of a continuous self-mapping on a topological space are discussed by applying the theory of open cover, invariant subset and non- d that if non-wandering set of the continuous self- , then the topological entropy of f is the same as that set, and the topological entropy of a continuous selfspace （X,T） is the same as that of the mapping on mapping on a strong θ-compact Hausdorff （X,θT））,where θ（T） is the set of all θ-open sets in （X,T）.

关 键 词：拓扑熵 非游荡集 θ-开集 θ-连续映射 

分 类 号：O189.1[理学—数学]