METRIZABILITY, MANIFOLDS AND HYPERSPACE TOPOLOGIES
This paper investigates metrization theory of manifolds in terms of hyperspaces. We prove that perfect hyperspaces are metrizable. We show that the problem whether the first countability of hyperspaces of a manifold implies the metrizability of the manifold is independent of ZFC.
Fell topology, finite topology, locally finite topology, manifold, metrizable, perfect.