Proof that Open Balls are Open Sets

[@johnq5507]

i can't believe this video has got only about 2k views. Such a great explanation! Greeting from Astana, Kazakhstan!

[@siriuss_]

7yrs mater it's 58k :)

[@DeiMuDon]

@@siriuss_ 62

[@gutzimmumdo4910]

thanks for the geometric interpretation and coloring it helps so much.

[@caglar1987]

This chanel is by far the best one.

[@anthonyluhumbika4693]

good explanations has give me confidence in functional analysis.

[@ouqassousouhayl7165]

Thank you for your videos sir, they are well explained, and please keep it on, you are really of a big help :)

[@fabriziogambelin8214]

This explanation is amazing! Thank you

[@sayanjitb]

Dear sir, what is the connection between the Metric space and Topology and Real analysis? could you please share your view? these some irresistible questions i carry out through my mind! Yours help would be appreciated.

[@flixerstudios1862]

Is this also possible without a notion of metric spaces (so just a topological space) since you seem to be using the triangle inequality which is a property of metric spaces but not of topological spaces (I guess since distance is not defined)?

[@debendragurung3033]

The Algebraic proof is sweet.

[@canadianthroneholder]

Very helpful thank you. Have you posted any videos showing that R^n is an open set?

[@cccookie4978]

Let x be any element of R^n. Then B(x, r) is contained in R^n (no matter what the value of r > 0 is.) Hence R^n is open.

[@goofydog07]

Even though you talk a bit like a rambler this is really helpful and clear thanks.

[@10010ist]

what about Sobolev space any lecture on these

[@MATSwatiGupta]

Is the converse of this statement true?

[@notyourordinarygamer1356]

Great video sir!

[@rampage14x13]

Very nice explanation thanks for sharing this

[@bigdreams7562]

i am not even done watching the video but man you super good. i stump that. thanks for this great video

[@paulus3523]

5.37, this is why I love maths

[@sarguxih]

excellent explanation! thanks

[@bobbistar7049]

I had blind math analysis professor. This is great

[@pyanamin1865]

awesome, thank you for such big help!

[@hamisiwenge9934]

great explanation vry helpful thanks much

[@EvangelineB6]

This is really well explained, thank you.

[@Mathpress]

great explanation....very useful..thank u sir

[@anldemirel8429]

eyvallah reyiz! Marvelous!

[@ankurpatil1]

nice explanation with figures...

[@tegan67]

Amazing explanation

[@martinkioko8286]

you look cute,,where do you study

[@kudakwashesoko5998]

Well explained

[@oliviahernandezlucio4941]

amazing, it was so clear

[@gagadosuhubert3756]

Finally, I got this

[@hariharan23998]

nice explanation superb sir

[@demetriomacias9578]

Thank you so much boss

[@zouhaierfridhi6713]

Amazing

[@perebonet6550]

you fucking genius I love you

[@vinivinix]

But is a ball just a kind of set though? So an open ball obviously is an open set.

[@젬레-q5y]

Thanks

[@globherman]

THANK YOU

[@hjchoi5368]

wow this guy is genius lol thank you!

[@rawiyahalraddadi942]

thanks

[@젬레-q5y]

god, you need a new highlighter

[@HL-iw1du]

How pointless

[@kudakwashesoko5998]

Well explained