An example of a compact space of uncountable character for which the space \(\exp_n(X)\setminus X\) is normal (Q887498)

Under Jensen's Axiom a compact, strongly hereditarily separable topological space \(X\) with uncountable character is constructed such that for each \(n\) the space exp\(_n(X)\setminus X\) is normal, where exp\(_n(X)\) is the space of subsets of \(X\) of cardinality at most \(n\) with the Vietoris topology and \(X\) is identified with the subspace of singletons. The underlying set of \(X\) is \(\omega_1+1\).