A scientific research device for geospace physics, the Space Plasma Environment Research Facility (SPERF), is going to be in operation this year at the Harbin Institute of Technology, China. One of its laboratory simulation platforms, the Asymmetric Reconnection EXperiment (AREX), is designed to investigate the asymmetric magnetic reconnection relevant to the process in the dayside magnetopause of the Earth. As a ground-based experimental platform, AREX emphasizes three-dimensional (3D) asymmetric driving features with topological similarity relevant to dayside reconnection. Thus, in this paper, we focus on topological analysis based on numerical simulation of AREX reconnection processes. 3D topological features in various scenarios relevant to magnetopause reconnection in different interplanetary magnetic field (IMF) conditions are investigated by adjusting setup parameters of plasma sources and magnetic coils. The simulation results reveal that the plasma distribution of asymmetric reconnection in SPERF-AREX is analogous to that at the magnetopause. Various types of the 3D magnetic topology relevant to typical IMF conditions, including the X-line and the A–B null chain structures, are, respectively, identified and analyzed in detail.