Abstract:In this paper we extend the notion of quasinormal convergence via ideals and consider the notion of $\mathcal{I}$-quasinormal convergence. We then introduce the notion of $\mathcal{I}QN~(\mathcal{I}wQN)$ space as a topological space in which every sequence of continuous real valued functions pointwise converging to $0$, is also $\mathcal{I}$-quasinormally convergent to $0$ (has a subsequence which is $\mathcal{I}$-quasinormally convergent to $0$) and make certain observations on those spaces.
Keywords: ideal, filter, $\mathcal{I}$-quasinormal convergence, Chain Condition, $AP$-ideal, $\mathcal{I}QN$ space, $\mathcal{I}wQN$ space
AMS Subject Classification: 54G99 54C30 40G15