Embeddings in the Fell and Wijsman topologies


Ĺubica Holá




It is shown that if a T 2 topological space X contains a closed uncountable discrete subspace, then the spaces (ω 1 + 1) ω and (ω 1 + 1) ω 1 embed into (CL(X), τ F), the hyperspace of nonempty closed subsets of X equipped with the Fell topology. If (X, d) is a non-separable perfect topological space, then (ω 1 + 1) ω and (ω 1 + 1) ω 1 embed into (CL(X), τ w(d)), the hyperspace of nonempty closed subsets of X equipped with the Wijsman topology, giving a partial answer to the Question 3.4 in [2]