This is episode 11 of a course on algebraic topology.
We motivate the proof of the excision axiom for singular homology. Proof details are given modulo a proof of the lemma of small simplices.
Previous video: https://youtu.be/WEPz7JCh5J4
Next video: https://youtu.be/ULjeeYdVfZk
Outline:
00:00 Start
02:26 Def.: 𝒰-small
07:32 Lemma of small simplices
10:35 Proof of excision axiom based on the lemma of simplices
25:06 Idea of the lemma of small simplices
