Exploring the Difference Paralindelöf in Topological Spaces

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DOI: https://doi.org/10.28924/2291-8639-23-2025-24
Published: Jan 27, 2025
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Ali A. Atoom, Rahmeh Alrababah, Maryam Alholi, Hamza Qoqazeh, Abeer Alnana, Diana Amin Mahmoud, Exploring the Difference Paralindelöf in Topological Spaces, Int. J. Anal. Appl., 23 (2025), 24.

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Ali A. Atoom, Rahmeh Alrababah, Maryam Alholi, Hamza Qoqazeh, Abeer Alnana, Diana Amin Mahmoud

Abstract

This study investigates emerging concepts for defining and categorizing topological spaces based on various features. Paralindelöf spaces are one such idea that is required to understand the compactness and covering features of topological spaces. This study is the first to introduce D-paralindelöf spaces, a novel type of topological space defined combining D-sets and paralindelöf spaces. The study's goal is to offer precise definitions for paralindelöf spaces and D-paralindelöf spaces, while also investigating their properties and linkages with other forms of topological spaces. The study contains various theoretical conclusions, definitions, and features that are rigorously proven by extending previous theorems on paralindelöf spaces. It is further backed by extensive illustrative examples.

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