A non-2-starcompact, pseudocompact Tychonoff space whose hyperspace is 2-starcompact

For a topological space X, let H ( X ) be the collection of all nonempty closed subsets of X with the Vietoris topology and let C ( X ) be the collection of all nonempty compact subsets of X equipped with the subspace topology. ve the following:(1) X ) is 1-starcompact, then X is K -starcompact; X ) is 1 1 2 -starcompact, then X is 1 1 2 -starcompact; and s a regular space which has a closed discrete subset E such that | E | = w ( X ) ⩾ ω , then C ( X ) is not 1 1 2 -starcompact, where w ( X ) is the weight of X. show that there exists a non-2-starcompact, pseudocompact Tychonoff space X whose hyperspace H ( X ) is 2-starcompact under the assumption p = c .