Geodesic
Spaces not distinguishing pointwise and $\mathcal{I}$-quasinormal convergence
Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 83-96 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 40G15, 54C30, 54G99
Keywords: ideal; filter; $\mathcal{I}$-quasinormal convergence; Chain Condition; $AP$-ideal; $\mathcal{I}QN$ space; $\mathcal{I}wQN$ space 
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     title = {Spaces not distinguishing pointwise and $\mathcal{I}$-quasinormal convergence},
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     year = {2013},
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}
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Das, Pratulananda; Chandra, Debraj. Spaces not distinguishing pointwise and $\mathcal{I}$-quasinormal convergence. Commentationes Mathematicae Universitatis Carolinae, Tome 54 (2013) no. 1, pp. 83-96. http://geodesic.mathdoc.fr/item/CMUC_2013_54_1_a6/