On a conjecture of Conley
The authors deal with a conjecture of Conley on the semicontinuity of the nonwandering set function. The authors give a partial answer to this conjecture. Indeed, they first prove the upper semicontinuity of the chain recurrent set function. Next, the authors prove that the set of points where the nonwandering set and the chain recurrent set coincide is contained in the set of points of upper semicontinuity of the nonwandering set function. However, it is not generally contained in the set of points of lower semicontinuity of the nonwandering set function.
scientific article; zbMATH DE number 2077275