Note about Fixed Points of Scott Continuous Self-Mappings

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.