Journal of E - Technology Sonja B. Chalamani, Elena T Kotevska, Marzanna J. Seweryn- Kumanovska 14 3 2023 https://doi.org/10.6025/jet/2023/14/3/76-81 https://www.dline.info/jet/fulltext/v14n3/jetv14n3_2.pdf We constructed a crucial type of Hilbert Space with a new approach. We have explained the 3,2,p -N-symmetrizable Hilbert space with a set of (3,2,p)-metric d on it. The proposed Hilbert Space has significant topological structure and properties. Thus, the special topologies we suggested are able to add to the notion of metric spaces.