Then we solve negatively Problem 1.11 which was posed by C.P.Niculescu,and a sufficient condition for this is given which generalizes Pelczyński's result.
In this paper,the topological Markov chain has been discussed.First,we introduce a structure of the directed gragh on a 0,1-matrix,and then by using it as a tool,we give some equivalent conditions with respect to the relationship among topological entropy,chaos,the nonwandering set,the set of periodic points and the 0,1-matrix involved.