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Spaces not distinguishing pointwise and $ℐ$ -quasinormal convergence

Pratulananda Das; Debraj Chandra — 2013

Commentationes Mathematicae Universitatis Carolinae

In this paper we extend the notion of quasinormal convergence via ideals and consider the notion of $ℐ$ -quasinormal convergence. We then introduce the notion of $ℐ Q N (ℐ w Q N)$ space as a topological space in which every sequence of continuous real valued functions pointwise converging to $0$ , is also $ℐ$ -quasinormally convergent to $0$ (has a subsequence which is $ℐ$ -quasinormally convergent to $0$ ) and make certain observations on those spaces.

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Spaces not distinguishing pointwise and ℐ -quasinormal convergence

Spaces not distinguishing pointwise and $ℐ$ -quasinormal convergence