On Well-filteredness Of Scott Power Spaces

In this paper,the concept of Scott power spaces of T₀ spaces is introduced and the well-filteredness of Scott power spaces is discussed.It is proved that if a T₀ space X is well-filtered,then its Scott power space?K(X)is well-filtered.Conversely,if the upper Vietoris topology is coarser than the Scott topology on the poset K(X)of all compact saturated subsets of X(endowed with the Smyth order)and?K(X)is well-filtered,then X is well-filtered.An example is given to show that there is a non-well-filtered space X for which its Scott power space?K(X)is well-filtered.