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Algebraic and topological foundations of non-Newtonian analysis via generator functionsCivgin, EmreYalcin, Numanalgebraic structuresalpha generator functionstar operatorsstar vector spacetopological structuresIn this paper we explored the algebraic and topological underpinnings of non-Newtonian analysis through the framework of a generator function α. We introduced the α-number systems and the associated arithmetic operations, and we established the corresponding algebraic structures, including groups, fields, and vector spaces defined over α-real numbers. On the topological side, we developed the notions of α-metric spaces and α-sequences, thereby extending core concepts of analysis to the non-Newtonian setting. The study culminates with the formulation of star (*) analysis, which provides a systematic mechanism for transitioning between distinct arithmetic systems, together with a rigorous treatment of *-vector spaces and linear operators.American Institute of Mathematical Sciences2025Articlehttps://rdlopen.rawdatalibrary.net/r/gumushane/13954https://doi.org/10.3934/math.202511712473-6988enAIMS Mathematicsinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://gumushane-rdlopen.rawdatalibrary.net/tr/items/gumushane/13954