Structural properties of pairwise difference Lindelöf spaces: statistical applications in data analysis
Resumen
This paper formalizes D-Lindelöf spaces in bitopological spaces, extending Lindelöf concept through D-sets. Key contributions include proving countable spaces are generally pairwise D-Lindelöf; establishing that pairwise D-Lindelöfness implies 1- Lindelöfness; demonstrating closure of D-sets under finite intersections; and analyzing
preservation under pairwise continuous surjections, D-irresolute functions, and perfect functions. The inheritance conditions for 1-closed subspaces are determined, with limitations clarified by counterexamples. Beyond theory, we demonstrate statistical applications: (i) D-set classification for mixed-feature data, (ii) convergence analysis under dual topologies, (iii) D-compactness in probability measures, and (iv) parameter identification modeling.
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