TOPOLOGICAL EXPLORATIONS: UNVEILING THE REALM OF CONTINUOUS FUNCTIONS AND THEIR COMPUTATIONAL APPLICATIONS
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Abstract
This paper delves into the fascinating realm of topology, specifically focusing on continuous functions and their computational applications. Topology, a branch of mathematics, provides a powerful framework for studying spatial relations and continuity. In this paper, we explore the foundational concepts of topology, elucidating the significance of continuous functions in various mathematical and real-world contexts. Additionally, we delve into the computational applications of continuous functions, showcasing their relevance in diverse fields such as computer science, physics, engineering, signal processing, geometric modeling, topological data analysis, dynamical systems, and chaos theory
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References
Munkres, J. R. (2000). Topology (2nd ed.). Prentice Hall.
Hatcher, A. (2002). Algebraic Topology. Cambridge University Press.
Kelley, J. L. (1955). General Topology. Van Nostrand.
Rudin, W. (1976). Principles of Mathematical Analysis (3rd ed.). McGraw-Hill.
Lee, J. M. (2011). Introduction to Topological Manifolds. Springer.
Engelking, R. (1977). General Topology. PWN, Warsaw.
Dugundji, J. (1966). Topology. Allyn and Bacon.
Spanier, E. H. (1966). Algebraic Topology. McGraw-Hill.
Willard, S. (1970). General Topology. Addison-Wesley.
Hocking, J. G., & Young, G. S. (1961). Topology. Addison-Wesley.
Dieudonné, J. (1960). A History of Algebraic and Differential Topology, 1900-1960. Birkhäuser.
Bourbaki, N. (1989). General Topology, Chapters 1-4. Springer.
Milnor, J. (1965). Topology from the Differentiable Viewpoint. Princeton University Press.
Steenrod, N. (1951). The Topology of Fibre Bundles. Princeton University Press.
Hatcher, A. (2005). Higher Algebraic K-Theory: An Overview. arXiv preprint math/0509023.