This manuscript presents innovative rough approximation operators based on an abstract structure called “minimal topology”. This approach offers greater flexibility than traditional topological frameworks by removing the conventional closure requirements for unions and intersections inherent in standard topology, thereby expanding its applicability. We construct eight types of minimal topologies using Nκ-neighborhood systems and the concept of primals. The relationships between these topologies are examined, with a focus on identifying conditions under which they are equivalent. New rough-set models are derived from these minimal topologies, and key properties of their lower and upper approximations are established. Additionally, we apply these approximations to classify subset regions and compute their accuracy measures.