The persistent homology computation on a triangulated (n)‑manifold with (N) simplices runs in (\mathcalO(N \log N)) time and (\mathcalO(N)) space, improving upon the classic (\mathcalO(N^2)) bound.
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Abstracting the concept of distance to study convergence and continuity. Abstracting the concept of distance to study convergence
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is a core branch of modern mathematics. It investigates the properties of geometric shapes that remain unchanged under continuous deformations like stretching, twisting, and crumpling. Unlike traditional geometry, topology disregards measurements like distances and angles, focusing instead on the fundamental connectivity of spaces.
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: The text provides an exposition of both general (point-set) and algebraic topology, covering topological spaces, compactness, connectedness, completeness, metrizability, and algebraic aspects like homotopy and homology groups. Google Books Access and Downloads