Compactness

The single, most important concept in topology and analysis: Compactness. This is explained via covers, which I'll define as well. There are tons of applications of this concept, which you can find in the playlist below

[blindhouse]

At the end of 2020 I started watching your videos. The best is that I watch just for entertaining. I don't have any exams or studying maths

[djvalentedochp]

colorful thumbnails are the most enthralling ones, I can't resist!

[andreutormos]

I was struggling with concept of compactness in Real Analysis classes, where my teacher won't stop naming it. This month I have my finals, so thank you very much for this video and every single other video! :D I will watch it later today

[mightym]

This is maths sounding history class and we all listen wide open... thank you so much!

[umerfarooq]

Just when mathematics is about to make me crazy your channel keeps me sane, you surprise me by how easy you make maths

[marcossful]

You inspire me. What a remarkable video. Helped me a lot to gain the intuiton. Thank you so much

[nocomment]

I think this is my favorite video on the channel, it does a brilliant job at building the intuition for the definition of compactness.

[iabervon]

I was listening to a finite subcover band recently. They'd done every song I could think of, until I started looking for songs that were only digital downloads. It turned out that they'd only necessary done a song if it came out on a compact disc...

[RalphDratman]

I enjoy this way of learning math, because it is varied rather than strictly progressive -- and I never have to take an exam! 
In other words, over time your videos are something like an open cover for the open set of things I want to learn.
That is perfect for my randomly wandering mind! My wishes are scattered and so is the cover. THANK YOU
(But the property of being compact seems strange to me.)

[mokopa]

Today Dr Peyam taught me that inside jokes are compact.

[rajashreedabre]

Thank you very much as my confusion about compactness is cleared just because of diagrammatic explaination

[suhaibalkhaldi]

Dr.Peyam thank you very very much for the efforts you put in your videos, you have a great ability of delivering the information is a simple way .

[ThobelaGoge]

I finally found a video that makes it more clear....Thanks man

[camileclere]

your videos are so much fun and so educational

[mertaliyigit]

Hey Peyam, as I learn more about maths, ln(x) and e^x functions became more impressive to me. Its pretty thrilling that those functions are opposite of each other. Can you prove those functions are opposite of each other, maybe using calculus or infinite sums (though that one seems impossible)?

[tino_]

whenever i would struggle with something in my analysis class i just come to your channel and everything becomes clear :) thank you so much

[wenanyaugustine]

If there was rating i would give 5 star with the best comment i can give. Damn this nija is crazy good at this . Its like a play . I enjoy watching

[ecologypig]

Thanks for your super helpful lectures, Dr. Peyam. I like how you always give many positive as well as counter-examples to every concept. Even though I have learned some of these concepts in my undergraduate days, your videos often provide new and intuitive angles.

[pranjaliaggarwal]

One of the best channels!!!
Amazing explanation sir💯💯

[アナキンスカイオ一カ]

Utilizing this concept, I demonstrated that it is possible to prove the existence of a boundary of a ball by means of the information that it is coverable in all of its parts. However, it turns out that the axiom of the choice is used and it may be not been considered as valid as it would be without it.