English

Embeddings in the Fell and Wijsman topologies

General Topology 2015-08-28 v2

Abstract

It is shown that if a T2T_2 topological space XX contains a closed uncountable discrete subspace, then the spaces (ω1+1)ω(\omega_1 + 1)^{\omega} and (ω1+1)ω1(\omega_1 + 1)^{\omega_1} embed into (CL(X),τF)(CL(X),\tau_F), the hyperspace of nonempty closed subsets of XX equipped with the Fell topology. If (X,d)(X,d) is a non-separable perfect topological space, then (ω1+1)ω(\omega_1 + 1)^{\omega} and (ω1+1)ω1(\omega_1 + 1)^{\omega_1} embed into (CL(X),τw(d))(CL(X),\tau_{w(d)}), the hyperspace of nonempty closed subsets of XX equipped with the Wijsman topology, giving a partial answer to the Question 3.4 in [CJ].

Keywords

Cite

@article{arxiv.1508.06441,
  title  = {Embeddings in the Fell and Wijsman topologies},
  author = {Lubica Hola},
  journal= {arXiv preprint arXiv:1508.06441},
  year   = {2015}
}