<p>Topological structures play a crucial role in representing relational systems across mathematics and applied sciences. In recent years, efforts to enhance the expressiveness of topological frameworks have led to the integration of advanced uncertainty models. This paper investigates topological structures constructed on virtual fuzzy parameterized soft (vfps) set theory, a novel hybrid framework designed to address limitations in existing models regarding the expression of membership uncertainty. The vfps-set model allows decision-makers to specify both lower and upper approximations for each membership degree, thereby capturing potential error margins in their evaluations. This tri-level representation—comprising lower, ideal, and upper fps-sets—enables more robust modeling of imprecise or subjective information. Leveraging this advantage, the paper introduces and studies several fundamental components necessary for building vfps-topological spaces, including generalized intersections and unions, vfps-points, quasi-coincidence, and vfps-mappings. Using these foundational tools, the concept of a vfps-topology is formally defined. Subsequently, classical topological notions such as openness, closedness, closure, interior, neighborhoods, continuity, base systems, covers, and compactness are extended to the vfps framework. Relevant properties and illustrative examples are provided to clarify each concept. The resulting structure offers a flexible and powerful tool for uncertainty modeling in both theoretical and applied contexts.</p>