The Baire Category Theorem

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In this video, I try to prove the Baire category theorem. I will first define metric spaces and completeness of metric spaces, then look at the topology of metric spaces, and finally prove the theorem itself.

Hello~ I am MeeMee GuLu, a homeschooled student in Taiwan. I care about the environment and love math.

MeeMee GuLu

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The preparations and behind the scenes segments were really cute. Great explanation too. Thank you, and greetings from Mexico

vladimirmarquez

Thank you! I didn't understand the proof in my functional analysis course, and with this video I have been able to fill out the missing links!

TheWombatGuru

Thank you for the proof! However, I have just a comment. Instead of just reading the mathematical notation and the mathematical statements, try to explain what do they mean in plain words (both algebraically and geometrically). This will probably help a lot to digest the definitions and intentions of each step of the proof.

caio

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