Application of New Neutrosophic Open Set via Neutrosophic Topological Spaces

We introduce a new class of open sets in neutrosophic topological spaces, called neutrosophic Iopen (NI-open) sets, together with their dual NI-closed sets, defined via neutrosophic δ-interior and δ-closure operators. We establish basic stability (arbitrary unions of NI-open sets and arbitrary intersections of NI-closed sets), give characterizations in terms of the associated interior/closure operators, and prove a decomposition formula expressing every NI-open set as the union of its NδS-int...

New Classes of δ − β∗-Continuous Mappings in m-Polar Neutrosophic Topological Spaces

We introduce and study two classes of neutrosophic continuous mappings: the neutrosophic irresolute δ−β∗-continuous mappings (NIr δ−β∗ CM) and the neutrosophic contra δ−β∗-continuous mappings (NC δ−β∗ CM). We establish their fundamental properties and provide characterizations in terms of preimages of δ−β∗-open and δ−β∗-closed sets. The interplay between the two notions is analyzed through implication chains, (non-)equivalences under mild hypotheses, and stability results under composition, s...

Compactness Theory in Complex Neutrosophic Soft Spaces and Its Application to Visual Cosine Similarity Analysis

In the framework of complex neutrosophic soft topology, the paper investigates locally compact spaces and complex neutrosophic soft compact spaces. Complex neutrosophic soft open covers, finite sub-covers, closed set intersections, centered families, and several comparable requirements are used to define the idea of compactness. Compact subsets of Hausdorff space were shown to be closed, and compact Hausdorff spaces were shown to be normal. The relationships between compactness axioms, closed...

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