On the Reznichenko and Pytkeev properties in hyperspaces (Q6182712)

In this paper the authors deal with two properties: the Reznichenko and the Pytkeev properties. The first was introduced by Reznichenko in 1996 using the name weak Fréchet-Urysohn property and the second by Pytkeev in 1984. A space with the Pytkeev property has the Reznichenko property and these properties are intermediate between sequentiality and the countable tightness property. Here the authors present some characterizations of Reznichenko and Pytkeev properties in the hyperspace \(CL(X)\) of a space \(X\), consisting of all non-empty closed subsets of \(X\) endowed with the hit-and-miss topology with respect to \(\Delta\), where \(\Delta\subseteq CL(X)\) is a subfamily of \(CL(X)\) closed under finite unions and containing all singletons.