在随机集与模糊落影的研究中,需要将可测结构从论域向幂上提升。这一思想使我们把对超拓扑的研究与拓扑结构的提升联系起来,并且得到了一些初步的结果。面对这些结果,不禁使我们回过头来更深入地探讨了拓扑结构与序结构的关系,产生了扩展、推广经典拓扑的思想。也受fuzzy拓扑研究中我国“无点化”流派的启发,最终地,我们在完全格上建立了格化拓扑这一较广的理论框架。 In the research of random set and fuzzy falling shadow, we need to improve the measurable structure from the universe of discourse to the power. This idea led us to link the study of the hyper-topology with the improvement of the topology, and some initial results were obtained. Faced with these results, we can not help but look back and explore the relationship between topological structure and ordered structure in more depth, resulting in the idea of ​​extending and popularizing classical topologies. But also inspired by the “pointless” genre in the research of fuzzy topography. Ultimately, we have established the broader theoretical framework of the lattice topology on the complete lattice.