Baire Category Theorem

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The celebrated Baire Category Theorem in topology, which answers the following question: Is the intersection of open dense sets dense? If your space is complete, then the answer is yes. Come and enjoy this beautiful excursion in the world of topology!

Dr Peyam

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Thanks for such a great content with love from India

shivaudaiyar

go bears!!! im currently learning this in math 104 (introduction to real analysis) at berkeley, and your videos are actually amazing

AntonioMac

Nice video excellent method of teaching actually makes the student want to listen being an absent minded one myself I'm surprised

umerfarooq

Very nice. I heard this proof before in class, but it got foggy after we used completness. Thank you for clearing it up.

Domzies

You are a phenomenal teacher Sir ! Thank you for making our life simpler.

JhaaJii

That Kilmt makes for a great background.

BogdanBocse

I'm new to this, but Quick Question: You write that we WTS that (1) B intersects every Un, meaning that (2) there is a y in B that intersects every Un. I understand that (2) => (1) so if we prove (2) we are done. But it doesn't seem to me that the two are equivalent.

bentupper

Great . You have to teach my doctor so that he might be like you!!

ahmedmghabat

It is nice as it starts from scratch and I don't have to Google meaning of the terms

adityadwivedi

thank you so much, but I am struggling with approving that the intersection is of second category in R. Maybe If should also prove that the intersection is open?

iman

My analysis final just ended a few days ago. Only if this would've happened just a few days earlier 🤯

vrowniediamond

Wait, is a closed ball in a complete metric space guaranteed to be compact?

I always forget which results I know for R^n vs more general situations.

martinepstein

bro, I don't even see a single category here 🤣 Slightly disappointed

shiina_mahiru_

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