Bagirmaz, NurettinBağırmaz, Nurettin17.03. Department of Electronics and Automatization / Elektronik ve Otomasyon Bölümü17. Vocational Higher School / Meslek Yüksekokulu01. Mardin Artuklu University / Mardin Artuklu Üniversitesi2025-02-152025-02-1520242473-6988https://doi.org/10.3934/math.20241435https://hdl.handle.net/20.500.12514/6126bagirmaz, nurettin/0000-0002-7663-3002This study presents a novel approach to defining topological rough semigroups on an approximation space. The concepts of topological space and rough semigroup are naturally combined to achieve this goal. Also, some basic results and examples are presented. Furthermore, some compactness properties are also studied. In addition, their rough subsemigroups and rough ideals areen10.3934/math.20241435info:eu-repo/semantics/openAccessRough SetsRough SemigroupRough IdealTopological SemigroupTopological RoughSemigroupArticle2-s2.0-852081044440