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Introduction to Metric Spaces

467 ratings | 75227 views
The axiomatic description of a metric space is given.
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RatmirMugattaro (1 month ago)
1. Thank you for explaining but 2. I believe it would be even better if you instead of reading letters, read the actual meaning. Example: instead of "for all epsilon greater than zero... if little n greater than big N..." the actual meaning is " No matter how small I chose the positive value of epsilon I can always find the Number of the element after which the all the consecutive elements will be no further than epsilon distance from my limit value." It might seem little difference here but in more complicated concepts it helps to understand. 3. For some listeners might help to mention the life implication like: I am a sequence and I want to be that close in my relationships to, say, Ashley. So no matter how close I want to be to her (kissing or sleeping) there exists a certain number of dates I have to go out with her so after that we get as close as I wanted.
Clark Makmur (1 month ago)
just finished the whole series, Awesome and really helpful videos!
Ты можешь использовать только три теоремы: 1) d(x, x) = 0 2) d(x,y) = d(y,x) 3) d(x,y) < d(x, z) + d(z,y). Используя их можешь получить d(x,y)>0. https://ru.wikibooks.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%B9_%D0%B4%D0%B5%D0%B9%D1%81%D1%82%D0%B2%D0%B8%D1%82%D0%B5%D0%BB%D1%8C%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BF%D0%B5%D1%80%D0%B5%D0%BC%D0%B5%D0%BD%D0%BD%D0%BE%D0%B3%D0%BE/%D0%9C%D0%B5%D1%82%D1%80%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B5_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE
umar dari (2 months ago)
thanks sir
Topi Ado (2 months ago)
hats off to you sir👍👍👍
Osama I (3 months ago)
I failed two times in Metric spaces B.Sc Mathematics, but got 82% marks after watching your videos. The concepts are very clearly explained and east to understand
Philip Abolmoali (4 months ago)
soloutube1966 (5 months ago)
Your video's are saving me. I am a grad student in the dep. of Math and this video is my main reference.
Shahbaz Malik (7 months ago)
you are fantestic job
akiru bamiru (9 months ago)
Greetings from Ukraine.
syed burhan (1 year ago)
Hello Sir ! could you please tell me that what are the abstract distance spaces other than metric and normed spaces ?
Aniket Deshpande (1 year ago)
Really appreciate what you are doing here ! Keep making such videos. This one made me understand the subject better. Thanks. :)
Sujan Kapadia (1 year ago)
Why does the distance between two members of a metric space map to a real number? The set of real numbers is itself (along with the Euclidean distance function) a metric space. In that case, how can real numbers be used to describe a property of real numbers?
CORNuCoPia (1 year ago)
GREAT videos..concepts are made crystal clear. Thank you so much for uploading them.
Kajal A (1 year ago)
sir, can you please put a video explaining the proof of urysohn's lemma.
Navaron (1 year ago)
Kajal A he hasn't uploaded anything for 6 months
thank you a good reminder
you gotta work on closing curly bracecs
Stuart Morrow (1 year ago)
There's a good way to do that. *1. Start here* ` ` ' ' ` *2. Lift pen; go to v. bottom* ; *4. Done* ; : ; *3. i.e. here*
Alex Fan (1 year ago)
Thank you for the video. It really helps clear the concepts that I have been struggling for a long time.
Syed Adeel (2 years ago)
The triangle inequality has several useful consequences. Show that |d(w x) - d(x y)| =< d(w z) + d(z y)
David Hofmann (2 years ago)
very nicely explained! Thank you!
Musa Hamza (2 years ago)
Sir, Please tell me.. How to Determine whether the permutation is even or odd. Please reply me.. I am Waiting
Dauren Tolbassy (2 years ago)
what kind of book have you read for functional analysis
Dauren Tolbassy (2 years ago)
Hi, What kind of book do you advise for functional analysis
Paesan Ng (2 years ago)
You should do Calculus of Variations.
Komal Kharat (2 years ago)
The best teaching.after learning this my concepts are very cleared.....you make seem so easy with easy language.. THANK YOU SO SO MUCH
Ruoyu Chen (2 years ago)
Thank you for uploading the video! The graphic example of limit on the real line and the example of Cartesian product are very helpful.
HL (2 years ago)
Very eloquent video. Thanks for uploading!
Dalia Ramirez (2 years ago)
You make it seem so easy. Can you post more videos on d3:R^2*R^2---->R when d3(x,y)=min{1,d(x,y)}
Bma Muktadir (2 years ago)
I am really satisfied to receive such nicely presentation movie clips & animation to review my early life accumulated knowledge. I update my lost idea & renovate again my confused ideas. Thank to all gentle people who created such entertain knowledge world.
Pankaj Rai (2 years ago)
Is it not very similar to Cauchy sequence? I am confused now.. kindly somebody state the difference.
do it annammo (2 years ago)
vry helpful
Joey Ulseth (2 years ago)
Absolutely phenomenal explanations. Thank you so much for the time you put into all of your videos.
Eddie Main (3 years ago)
I like your videos !
Shehan.Seneve (3 years ago)
You are better than my lecturer who has a PhD. I wish you all the best in doing these videos.And it would be great if you could do a series on complex analysis and Integration in real analysis.
Jonathan Keam (3 years ago)
Fantastic job explaining.  Kudos!
Maryam A (3 years ago)
AMAZING THANK YOU . wouldve been better if you sequenced your all topology videos in an order . 

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