An embedding in the Fell topology

Abstract

Using a result from [7] it is shown that if a T2 topological space X contains a closed uncountable discrete subspace, then the space ω1×(ω1+1) embeds as a closed subspace of (CL(X), τF), the hyperspace of nonempty closed subsets of X equipped with the Fell topology. We will use the above result to give a partial answer to the Question 3.8 in [2].