Topological position of a point with respect to a set in a raw bistruct

In this study, we investigate the topological positions of points relative to sets in various topologies induced by raw binary operations. The fact that the raw binary operation is weaker than both partial and multivalued ones allows for a relatively wider variety of topologies induced by it. This gives us the ability to determine the topological positions of a point in a raw binary structure relative to a set by considering the lo-topology, ro-topology, and o-topology induced by the raw binary operation. Through the analysis of topological positions such as interior points, limit points, and closure points, we gain a deeper understanding of the nature of raw binary operations from a topological perspective. The potential benefit of this work is to expand the conceptual framework in terms of topological evaluability of problems in algebraic structures. In this study, we introduce the concepts of raw-binary interior point, raw-binary limit point, raw-binary closure point and give some useful facts about finding raw-binary interior, raw-binary limit and raw-binary closure points of a given set in lo-topology, ro-topology and o-topology. The potential benefit of this study is to provide topological evaluability of problems in algebraic structures by extending the conceptual framework.