Collectionwise Pre-Normality in Topological Spaces (European Journal of Pure and Applied Mathematics, 2025)
This paper introduces and studies a new topological property called collectionwise pre-normality. A space X is said to be collectionwise pre-normal if and only if X is T1 and for every discrete family F = Fss∈S of closed subsets of X, there exists a discrete family U = Uss∈S of pre-open subsets of X such that Fs ⊆ Us for each s ∈ S. We investigate this property and presentexamples that illustrate its relationship with other known topological properties.
Keywords: collectionwise normal, paracompact, pre-normal, discrete family