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146 | Emily Riehl on Topology, Categories, and the Future of Mathematics

Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas

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Exploring Topology: From Coffee Cups to Tori

This chapter explores the fascinating field of topology, focusing on concepts such as homeomorphism and homotopy equivalence. By using engaging examples like a coffee cup and a torus, it illustrates how seemingly different shapes can be transformed into one another through continuous deformations. The discussion emphasizes the interplay between algebra and geometry, highlighting the practical implications of these topological ideas in areas like particle physics.

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