On the Topological Foundations of Metric Case Spaces (MCS) In Computational Jurimetrics

Ogbonna Nnamuchi

doi:10.56201/ijcsmt.vol.12.no5.2026.pg162.166

📄 Download Paper

On the Topological Foundations of Metric Case Spaces (MCS) In Computational Jurimetrics

Ogbonna Nnamuchi

Abstract

Recent paradigms in computational law have demonstrated that abstract legal concepts can be mapped into mathematically robust frameworks. Building upon the foundational formulation of Jurimetric Spaces and Metric Case Spaces , this paper investigates the intrinsic topological properties that govern collections of legal precedents. By treating judicial decisions as distinct points within a metric-adapted environment, we systematically address a vital theoretical question: What is the exact mathematical nature of the topology induced on a set of case laws? We formally define a metric-induced legal topology, prove that standard metric-to-topology transitions preserve essential point-set properties on case domains, and construct a generalized verification model for n-dimensional legal case configurations. Finally, we explore the structural implications of these topological properties on legal proximity, case law convergence, and automated judicial retrieval systems.

Keywords

Computational JurisprudenceJurimetricsMathematical LawMetric Case SpacesLegal TopologyPoint-Set Topology.

References

[1] Baryse ̇, D. (2022). People’s attitudes towards technologies in courts. Laws, 11(5), 71. https://doi.org/10.3390/laws11050071 [2] Gruginskie, L. A. d. S., & Vaccaro, G. L. R. (2018). Lawsuit lead time prediction: Comparison of data mining techniques based on categorical response variable. PLOS ONE, 13(6), e0198122. https://doi.org/10.1371/journal.pone.0198122 [3] Koniaris, M., Anagnostopoulos, I., & Vassiliou, Y. (2015). Network analysis in the legal domain: A complex model for European Union legal sources. arXiv. https://doi.org/10. 1093/comnet/cnx029 [4] Rhim, Y.-Y., & Park, K. (2019). The applicability of artificial intelligence in international law. Journal of East Asia and International Law, 12(1), 7–30. https://doi.org/10.14330/ jeail.2019.12.1.01 [5] Stern, J. M., Pereira, C. A. d. B., Lauretto, M. d. S., Esteves, L. G., Izbicki, R., Stern, R. B., Diniz, M. A., & Borges, W. d. S. (2022). The e-value and the Full Bayesian Significance Test: Logical properties and philosophical consequences. arXiv. https://doi.org/10.48550/ arxiv.2205.08010

On the Topological Foundations of Metric Case Spaces (MCS) In Computational Jurimetrics

Abstract

Keywords

References

More Articles from INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND MATHEMATICAL THEORY