What is a continuous extension?

[@purim_sakamoto]

おおおー ちょうど連続写像とかの話を読んでたから、めっちゃ参考になるわぁああ ありがたいこっちゃでほんと😌🙏🙏🙏

[@rexdalit3504]

If memory serves, Hunt used projections onto Walsh distributions to finally pin down the convergence properties of Fourier transforms in the early 60s (or maybe 70s). Maybe you could make a special exception for them. (ps Hunt was a great hand ball player, but often Phelps was better; however, Hunt could understand the "corner walking" vibration functions for certain degenerate ball shots into the corners.)

[@juanmolinas]

Greetings Doc!, you explain very well, and your english is very clear!

[@mudkip_btw]

I prefer f "snek" for the tilde but "squiggle" works as well I guess

[@rounaksinha5309]

Very nice explanation,sir. Thank you very much!

[@sabhrant5533]

For those who are interested in this topic, you can refer to "Introduction to real analysis" by Bartle and Sherbet, 4th edition. The continuous extension thm is given on pages 144, 145. Sir, is it possible to extend this result to higher dimensions? (like the boundary of an open set.)

[@arturcostasteiner9735]

Yes. And also on the complex domain.

[@rikthecuber]

I don't know much on calc 3(except the very basics) but can you suggest me a video on cross product of 2 vectors w/o converting into components?

[@رشاداليامي]

Doctor , do you want to tell us new definition for cont ?

[@رشاداليامي]

Or definition cont on set bigger than last set

[@ZipplyZane]

I'm not sure I understand how an endpoint can be continuous. Can you have continuity on only one side? In other words, in the first example, can we say ~f is continuous at x=0 because lim_a->0+ (~f(a)) = ~f(0) ? Or is it only continuous because x sin(1/x) is continuous on all point of the interval (-1,0) as well?

[@drpeyam]

Yes, it’s called one sided continuity, so here f is continuous at 0 from the right

[@sparshsalodkar6177]

Glad I subscribed! ✌️🤝

[@HaCkeMatician]

Hello Dr.Peyam! I want to ask about the oscillating sequences: what is the mathematical importance of the central value of oscillation? Should we have to know its value? Thanks

[@sieni221]

Wow I just had this last week in topology class

[@رشاداليامي]

We redefine the function on the extended set to get the extended connection Is correct doctor?

[@arturcostasteiner9735]

Yes.

[@6612770]

I expected the proof to use reliance on a Limit existing AND all derivatives existing, as you approach the end of the domain segment.

[@flowers9652]

Hello sir, thank you very much for the videos they are very very helpful for clearing the concept, but I have a doubt in this last minutes of the video you showed that if x -> a then (f^~)(x) -> (f^~)(a), I completely understand the part where you showed that the limit exists and is unique irrespective of the sequence we choose, but I have doubt that how can we be sure that the limit say S obtained is same as (f^~)(a), I.e. S = (f^~)(a)......???? Waiting for you reply.. Thank you😇😇

[@dr.rahulgupta7573]

Very good lecture. Thanks Dr 3.14159....m .

[@satishr8288]

Here is an interesting question I came across ' how many Spheres of 1 cm radius will fit inside larger hollow sphere of 1meter'.

[@chrisglosser7318]

Tune in for the math, stay for the dad jokes :-)

[@shahinjahanlu2199]

Sometimes life is just sinx/x near zero

[@drpeyam]

Hahaha

[@shahinjahanlu2199]

@@drpeyam باور کن

[@pierreabbat6157]

~f(0)=0 ~f(x)=sin(1/x), x∈(0,1) ~f(x)=sin(1)-(x-1)cos(1), x∈[1,∞) Also, what about analytic continuation?

[@EmissaryOfSmeagol]

Wow the Doc does not accept extensions, that's harsh haha

[@dgrandlapinblanc]

Not evident. Thank you very much.

[@rialtho_the_magnificent]

I was wondering how Oreo is doing?

[@drpeyam]

Oreo passed away in June 😞

[@irinaignatova1799]

Sorry for your loss :(

[@iabervon]

It's not hard to show that sin 1/x is not UC, Let delta be 2. For any epsilon, let k be the ceiling of 1/epsilon. Then let x be 2/π(4k+1) and y be 2/π(4k+3). |x-y| < epsilon and yet |f(x)-f(y)|=delta.

[@yoav613]

I think this video is just an excuse to say squiggle 😃😄