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2006•Journal of Chongqing University. English EditionRequires access

Spanning Set and Separating Set in Topological Dynamical System

Lin Yin-he

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Abstract

This paper first discusses the spanning sets and separating sets in Bowen-topological entropy,and obtains some characters about them:(1)f∈X,Xhas certainly limited(n,e)-spanning set;(2) Every(n+1,e)-spanning set is the(n,e)-spanning set;(3) Every(n,e)-separating set is the(n+1,e)-separating set;(4)Every(n,e)-separating set is a limited set.Finally,it discusses a character about the spanning set and separating set under the uniformly convergence.

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What this paper is about

This paper first discusses the spanning sets and separating sets in Bowen-topological entropy,and obtains some characters about them:(1)f∈X,Xhas certainly limited(n,e)-spanning set;(2) Every(n+1,e)-spanning set is the(n,e)-spanning set;(3) Every(n,e)-separating set is the(n+1,e)-separating set;(4)Every(n,e)-separating set is a limited set.Finally,it discusses a character about the spanning set and separating set under the uniformly convergence.

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Available abstract

This paper first discusses the spanning sets and separating sets in Bowen-topological entropy,and obtains some characters about them:(1)f∈X,Xhas certainly limited(n,e)-spanning set;(2) Every(n+1,e)-spanning set is the(n,e)-spanning set;(3) Every(n,e)-separating set is the(n+1,e)-separating set;(4)Every(n,e)-separating set is a limited set.Finally,it discusses a character about the spanning set and separating set under the uniformly convergence.

Key concepts: Connected dominating set, Set (abstract data type), Combinatorics, Mathematics, Spanning tree, Maximal independent set, Discrete mathematics, Independent set

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