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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 2

On Topologies Induced by Order Relations on Dual Numbers

Nurcan İlayda Kaya(KIRIKKALE UNIVERSITY)0000-0001-8966-5225
Buşra Aktaş(KIRIKKALE UNIVERSITY)0000-0002-1285-7250
Olgun Durmaz(ERZURUM TECHNICAL UNIVERSITY)0000-0002-0913-3307
Halit Gündoğan(KIRIKKALE UNIVERSITY)0000-0002-5806-2090
Pages
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Publication Date
2026-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

With the help of these relations, topologies have been constructed in the space $\mathbb{D}^n$, and the geometric modelings of some elements of these topologies have been carried out.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Inequalities are often utilized in different areas of mathematics to establish theorems.
📊
Key Findings & Data:The presence of inequalities plays a crucial role in the foundations of these branches.
💡
Conclusion & Impact:With the help of these relations, topologies have been constructed in the space $\mathbb{D}^n$, and the geometric modelings of some elements of these topologies have been carried out.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Dual numbers · dual inequalities · topology

Abstract

Inequalities are often utilized in different areas of mathematics to establish theorems. The presence of inequalities plays a crucial role in the foundations of these branches. In this study, we examine the properties of order relations in the dual number system, inspired by the characteristics of order relations defined on real numbers. With the help of these relations, topologies have been constructed in the space $\mathbb{D}^n$, and the geometric modelings of some elements of these topologies have been carried out.

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Cite This Article

Kaya, N. İ., Aktaş, B., Durmaz, O., Gündoğan, H. (2026). On Topologies Induced by Order Relations on Dual Numbers. Turkish Journal of Mathematics and Computer Science, Volume: 18 Issue: 2. https://doi.org/10.47000/tjmcs.1807698

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