In present paper we discuss several approaches to reconstructing the topology of the physical space from neural activity data of CA1 fields in mice hippocampus, in particular, having Cognitome theory of brain function in mind. In our experiments, animals were placed in different new environments and discovered these moving freely while their physical and neural activity was recorded. We test possible approaches to identifying place cell groups out of the observed CA1 neurons. We also test and discuss various methods of dimension reduction and topology reconstruction. In particular, two main strategies we focus on are the Nerve theorem and point cloud-based methods. Conclusions on the results of reconstruction are supported with illustrations and mathematical background which is also briefly discussed.