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Keywords:
ideal; filter; $\mathcal{I}$-quasinormal convergence; Chain Condition; $AP$-ideal; $\mathcal{I}QN$ space; $\mathcal{I}wQN$ space
ideal; filter; $\mathcal{I}$-quasinormal convergence; Chain Condition; $AP$-ideal; $\mathcal{I}QN$ space; $\mathcal{I}wQN$ space
Summary:
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.
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