Ideal quasi-normal convergence and related notions
Volume 146 / 2017
Abstract
Recently the second author and D. Chandra (2013) began to study the notion of ideal quasi-normal convergence and some topological notions defined by this convergence. We show how some properties of those notions depend on the ideal; sometimes, they are also equivalent to some property of the ideal. Moreover, we exhibit non-trivial cases when the new notion introduced by the ideal quasi-normal convergence is equivalent to the corresponding original notions. Some relations between the new notions for different ideals are investigated as well. Then we extend the characterization of some of the notions by convergence properties of the topological space ${\rm C}_p({X})$. Finally, we study the relation of the new convergences to the covering properties of the underlying topological space.
