Bagirmaz, Nurettin2025-02-152025-02-1520242473-6988https://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 RoughSemigroupArticle9102963329644Q1Q1WOS:0013547084000042-s2.0-852081044440