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@article{208119,
        author = {Smt. Deshmukh Naziya Sultana Khursheed Ahmed},
        title = {A Mathematical Investigation of the Halting Function and the Resolution of the Halting Paradox via Termination Analysis on Definite Topological Spaces},
        journal = {International Journal of Innovative Research in Technology},
        year = {2026},
        volume = {13},
        number = {4},
        pages = {429-436},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=208119},
        abstract = {One of the most essential topics dealing with computability theory and mathematical logic is the Halting Problem. According to classical computability theory, there is no universal function   that can decide whether an arbitrary program  halts or not on input  . A new mathematical framework for the existence of halting function over definite topological space   is proposed in this paper. The execution of the program is viewed as a continuous mapping  . The different computational states are defined as points of a topological space.
The issue analyzes the convergence, compactness, and fixed-point theory that analyzes if a program will terminate. A computational sequence  generated by
 
is said to terminate if there exists a stable point  such that
 
While a universal halting function is undecidable for general-purpose computational systems, halting functions exist for limited domains. These must be compact and finite state space topologies of the entire computational state space. The framework gives a non-convergence proof of a, which is the classical halting paradox.},
        keywords = {Halting Problem, Halting Function, Topological Spaces, Computability Theory, Program Termination, Mathematical Logic, Fixed Point Theory, Formal Verification.},
        month = {September},
        }