## Pratulananda Das, Debraj Chandra

*Spaces not distinguishing pointwise and $\mathcal{I}$-quasinormal convergence*

Comment.Math.Univ.Carolin. 54,1 (2013) 83-96.**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

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