Kinematics-type workspaces reflect the fundamental properties of cable-driven parallel robots (CDPRs). Interference-free workspace (IFW) defined based on interference-free conditions is an extensively studied kinematics-type workspace due to its general significance. However, in cluttered environments, interference-free conditions alone might be insufficient in excluding infeasible poses. To this end, this paper incorporates topological constraints into the workspace analysis of a CDPR. Linking number, a topological invariant, is introduced to quantify the topological constraints imposed by closed-loop structures of a CDPR and obstacles. Based on the topological constraints, the topology-feasible interference-free workspace (TFIFW) is proposed, building upon the IFW, to enhance the workspace analysis of a CDPR in a complex environment, and a corresponding TFIFW generation method is proposed. A case study is provided to highlight the importance of incorporating topological constraints into IFW to achieve an accurate and comprehensive analysis of the kinematics-type workspace of a CDPR.