On Covering Prosperities via Neutrosophic <i>e</i> ‐Open Set in Neutrosophic Topological Space

This research presents and explores a novel category of compactness in neutrosophic topological spaces (NTSs), termed neutrosophic e‐compact and neutrosophic locally e‐compact. This category is positioned within the frameworks of neutrosophic δ ‐semicompactness and neutrosophic δ ‐precompactness, while also encompassing neutrosophic β ‐compactness. We have derived multiple preservation properties and characterizations associated with neutrosophic e‐compactness, along with an examination of its images and preimages across various functions. Following an introduction to the fundamental concepts of neutrosophic sets and NTSs, we define e‐open sets, e‐continuity, and neutrosophic e ∗ ‐continuous in the context of neutrosophic theory, alongside other related findings regarding e‐continuity. Additionally, we have identified several preservation properties and characterizations pertinent to e‐compactness such as a neutrosophic e‐base and a neutrosophic e‐subbase.