Basic Topology 3

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Focusing on advanced topics in algebraic topology and fiber bundles, this volume serves as a comprehensive resource for both undergraduate and graduate mathematics students. It explores homotopy theory, homology and cohomology theories, and the Euler characteristic, while addressing classic problems like the Jordan curve theorem. The text emphasizes connections between homotopy and homology, and introduces an axiomatic approach inspired by Eilenberg and Steenrod. With extensive material, it fosters active learning and a deeper understanding of modern analysis, geometry, and algebra.