In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
It is discussed in this paper that under what conditions,for a continuous domain L,there is a Scott continuous self-mapping f:L→L such that the set of fixed points fix(f)is not continuous in the ordering induced by L...It is discussed in this paper that under what conditions,for a continuous domain L,there is a Scott continuous self-mapping f:L→L such that the set of fixed points fix(f)is not continuous in the ordering induced by L.For any algebraic domain L with a countable base and a smallest element,the problem presented by Huth is partially solved.Also,an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable self-mapping f,fix(f)is not the retract of L.展开更多
基金the National Natural Science Foundation of China (Grant. No. 10071053) the SFEM of China and the Project of "Excellent Scholars Crossing Centuries" of the Education Ministry of China.
文摘In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
基金Supported by the National Natural Science Foundation of China(Grant No.10571112)the National Key Project of Fundamental Research(Grant No.2002CB312200)
文摘It is discussed in this paper that under what conditions,for a continuous domain L,there is a Scott continuous self-mapping f:L→L such that the set of fixed points fix(f)is not continuous in the ordering induced by L.For any algebraic domain L with a countable base and a smallest element,the problem presented by Huth is partially solved.Also,an example is given and shows that there is a bounded complete domain L such that for any Scott continuous stable self-mapping f,fix(f)is not the retract of L.
