Aura Topological Spaces and Generalized Open Sets with Applications to Rough Sets, Sensor Networks, and Epidemic Modelling
Ahu Acikgoz

TL;DR
This paper introduces aura topological spaces, a new structure with a point-to-open-set assignment, exploring their properties and applications to rough sets, sensor networks, and epidemic modeling.
Contribution
It defines aura topological spaces, analyzes their closure operators and open sets, and applies these concepts to practical problems in data analysis and network modeling.
Findings
The aura-closure operator is additive but not idempotent.
Hierarchy of generalized open sets is fully characterized.
Applications include generalized rough set approximations, sensor coverage, and epidemic spread models.
Abstract
We equip a topological space with a function satisfying the single axiom . The resulting triple , which we call an aura topological space, provides a point-to-open-set assignment that differs from all existing auxiliary structures in topology. The aura-closure operator turns out to be an additive Cech closure operator; it satisfies extensivity, monotonicity, and finite additivity, but idempotency fails in general. Iterating transfinitely yields a Kuratowski closure whose topology satisfies . We introduce five classes of generalized open sets, determine their complete hierarchy, and…
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Taxonomy
TopicsRough Sets and Fuzzy Logic · Fuzzy and Soft Set Theory · Advanced Algebra and Logic
