Machine learning-based automated theorem verification of nano-semi-weakly generalized closed sets in nano-topological spaces

S. Sathya Priya; N. Nagaveni; R. Lavanya; R. Saveeth; S. Sathya Priya; N. Nagaveni; R. Lavanya; R. Saveeth

doi:10.3934/math.20251230

AIMS Mathematics

2025, Volume 10, Issue 11: 28004-28019. doi: 10.3934/math.20251230

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Research article

Machine learning-based automated theorem verification of nano-semi-weakly generalized closed sets in nano-topological spaces

1.
Department of Mathematics, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India
2.
Department of Computer Science & Engineering, Coimbatore Institute of Technology, Coimbatore 641014, Tamil Nadu, India

Received: 21 July 2025 Revised: 23 September 2025 Accepted: 23 October 2025 Published: 28 November 2025
MSC : 54A40, 68T07

This study introduces and investigates a new class of sets, termed nano-semi-weakly generalized closed sets (NSWG-CS), within the framework of nano-topological spaces (NTS). Their key properties, formal definitions, and relationships with other generalized closed sets are examined. To bridge theoretical insights with computational applications, we present a machine learning (ML)-based automated theorem verification system. A graph neural network model (GNN) is implemented to classify and validate the NSWG-CS by leveraging structured representations of subset relations. The model is trained on a synthetic dataset and achieves an accuracy of 86.7%, an F1-score of 85.4%, a recall of 83.2% and precision of 87.8%, demonstrating reliable and realistic performance. These findings highlight the feasibility of applying ML techniques to verify mathematical properties within nano-topological structures. The integration of nano-topology and artificial intelligence contributes to the broader field of computational mathematics and automated theorem verification.
- nano-topological spaces,
- nano-semi-weakly generalized closed sets,
- machine learning,
- graph neural networks,
- automated theorem verification
Citation: S. Sathya Priya, N. Nagaveni, R. Lavanya, R. Saveeth. Machine learning-based automated theorem verification of nano-semi-weakly generalized closed sets in nano-topological spaces[J]. AIMS Mathematics, 2025, 10(11): 28004-28019. doi: 10.3934/math.20251230

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Abstract

This study introduces and investigates a new class of sets, termed nano-semi-weakly generalized closed sets (NSWG-CS), within the framework of nano-topological spaces (NTS). Their key properties, formal definitions, and relationships with other generalized closed sets are examined. To bridge theoretical insights with computational applications, we present a machine learning (ML)-based automated theorem verification system. A graph neural network model (GNN) is implemented to classify and validate the NSWG-CS by leveraging structured representations of subset relations. The model is trained on a synthetic dataset and achieves an accuracy of 86.7%, an F1-score of 85.4%, a recall of 83.2% and precision of 87.8%, demonstrating reliable and realistic performance. These findings highlight the feasibility of applying ML techniques to verify mathematical properties within nano-topological structures. The integration of nano-topology and artificial intelligence contributes to the broader field of computational mathematics and automated theorem verification.

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