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This time, we'll explain the homology of spatial pairs! Table of Contents: 1. Definition 2. Exact Sequences of Pairs 3. Cutting Theorem 4. Specific Examples 5. The Good Pair Proposition 6. Graduate School Entrance Exam Problem (Waseda University, Institute for Advanced Science and Technology, 2026 Entrance Exam) 7. Outline of the Proof of the Cutting Theorem #Mathematics #Topology #AlgebraicTopology #Geometry X: https://x.com/harmonia246369 [References] Kyohei Kawasumi, Fundamentals of Topology, Vol. 1 https://amzn.to/4aq5QF0 Masterno! ~How to Enjoy Mathematics~ "An Easy-to-Understand Explanation of the Second Isomorphism Theorem" https://mathtano.com/isomorphism-theo... 🎧 Voice Used: VOICEVOX: Kasukabe Tsumugi, Nekozuka Bii, Sakura Miko https://voicevox.hiroshiba.jp/ 🎬 Software Used: YMM4 Lite / Goodnotes Graduate School Entrance Exam Experience (Note) Part 1 (Events of Each Month): https://note.com/246369/n/nab52eece3c6b Part 2 (Study Methods for Basic Subjects): https://note.com/246369/n/n72098a0bca05 Part 3 (Study Methods for Specialized Subjects (Geometry)): https://note.com/246369/n/n6459509ceb0b *The links in the description box include affiliate links. As an Amazon Associate, this channel earns revenue through eligible sales.

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