• Abdulkareem, H. D., Mohammed, R. A., & Ameen, Z. A. (2024). Connectedness of soft r-topological spaces. New Mathematics and Natural Computation, 20(1), 27–43.

My research interests lie in advanced areas of General and Abstract Topology, with particular emphasis on Soft Topology and Hyper Topology. These fields occupy an increasingly important position in contemporary mathematics by providing sophisticated frameworks for studying uncertainty, generalized structures, and non-classical topological systems.
In Soft Topology, my research focuses on the foundational and structural properties of soft topological spaces, including soft continuity, soft compactness, and soft separation axioms. This work builds upon soft set theory as a mathematical framework for modeling uncertainty and imprecision.
In Hyper Topology, I investigate topological structures defined on families of subsets, with particular interest in how classical topological concepts extend and evolve within hyperspace settings.
More broadly, my research seeks to deepen the theoretical understanding of these frameworks, explore their interconnections, and examine their potential contributions to generalized topological systems and contemporary mathematical analysis.

Since 2023, I have been a faculty member in the Department of Mathematics at the College of Basic Education, University of Duhok, where I teach undergraduate courses in Axiomatic and Geometric and Group Theory.
My teaching philosophy emphasizes the development of logical reasoning, abstract thinking, and rigorous problem-solving skills — competencies that are essential not only to mathematics but also to broader academic and intellectual growth. I employ inquiry-based and discussion-oriented teaching methods that encourage students to think critically, question assumptions, and develop deep conceptual understanding rather than rely solely on procedural techniques.
Beyond delivering course content, I am committed to fostering students’ confidence in working with abstract mathematical structures and to helping them recognize connections between mathematical theory and its wider applications across disciplines.

Since 2025, I have served as a supervisor for undergraduate fourth-year graduation projects in the Department of Mathematics at the College of Basic Education, University of Duhok. My supervisory work focuses primarily on Topology and Soft Topology, reflecting both my research interests and my commitment to undergraduate academic development.
In this role, I guide students through the full process of independent research — from formulating research questions and reviewing relevant mathematical literature to developing and presenting original results. I place particular emphasis on strengthening students’ mathematical reasoning, analytical precision, and capacity for independent scholarly inquiry, helping them build the foundations necessary for advanced study and future research in mathematics.
Through close mentorship, I aim to cultivate not only a deeper understanding of advanced topological concepts and their contemporary applications, but also the intellectual discipline and research competencies that characterize rigorous mathematical scholarship.

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