A generalization of core compact spaces

In this paper, for a fixed infinite cardinal ν, we give the notion of a ν-core compact space generalizing the notion of a core compact space. Also, on the family of all open subsets of a space Y (actually on a partially ordered set) we define a topology denoted by τν and calling ν-Scott topology. This topology defines on the set C(Y,Z) of all continuous functions of the space Y into a space Z a topology denoted by tν. Some relations between ν-core compact spaces and topologies τν and tν are given.