Volterra Spaces are re-visited

Abstract

In this paper, we investigate weakly Volterra spaces and relevant topological properties. New characterizations of weakly Volterra spaces are provided. An analogy of the well-known Banach category theorem in terms of Volterra properties is achieved. It is shown that every weakly Volterra homogeneous space is Volterra, and there exists a metrizable Baire space whose hyperspace of nonempty compact subsets endowed with the Vietoris topology is not weakly Volterra.