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Introduction to Metric Spaces

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The axiomatic description of a metric space is given.
Категория: Образование
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Текстовые комментарии (41)
debendra gurung (4 дня назад)
can anyone advice whats prequisite to understand this series or the motivation. Do we need some real analysis?
Ben1994 (4 дня назад)
A rigorous basis for geometry.
Taylor X (1 месяц назад)
Hi , are x y z three distinct points ? or we can have x=y=z or x=y or y=z or x=z in triangle inequalty ?
RatmirMugattaro (4 месяца назад)
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 (4 месяца назад)
just finished the whole series, Awesome and really helpful videos!
Михаил Горобец (4 месяца назад)
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 Tanimu (5 месяцев назад)
thanks sir
Topi Ado (6 месяцев назад)
hats off to you sir👍👍👍
Osama I (6 месяцев назад)
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 (7 месяцев назад)
soloutube1966 (8 месяцев назад)
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 (10 месяцев назад)
you are fantestic job
akiru bamiru (1 год назад)
Greetings from Ukraine.
syed burhan (1 год назад)
Hello Sir ! could you please tell me that what are the abstract distance spaces other than metric and normed spaces ?
Aniket Deshpande (1 год назад)
Really appreciate what you are doing here ! Keep making such videos. This one made me understand the subject better. Thanks. :)
Sujan Kapadia (1 год назад)
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 год назад)
GREAT videos..concepts are made crystal clear. Thank you so much for uploading them.
Kajal A (1 год назад)
sir, can you please put a video explaining the proof of urysohn's lemma.
Navaron (1 год назад)
Kajal A he hasn't uploaded anything for 6 months
Tendamudzimu Shihlangu (2 года назад)
thank you a good reminder
Fatih Erdem Kızılkaya (2 года назад)
you gotta work on closing curly bracecs
Stuart Morrow (1 год назад)
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 (2 года назад)
Thank you for the video. It really helps clear the concepts that I have been struggling for a long time.
Syed Adeel (2 года назад)
The triangle inequality has several useful consequences. Show that |d(w x) - d(x y)| =< d(w z) + d(z y)
David Hofmann (2 года назад)
very nicely explained! Thank you!
Musa Hamza (2 года назад)
Sir, Please tell me.. How to Determine whether the permutation is even or odd. Please reply me.. I am Waiting
Dauren Tolbassy (2 года назад)
what kind of book have you read for functional analysis
Dauren Tolbassy (2 года назад)
Hi, What kind of book do you advise for functional analysis
Paesan Ng (2 года назад)
You should do Calculus of Variations.
Komal Kharat (2 года назад)
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 года назад)
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 года назад)
Very eloquent video. Thanks for uploading!
Dalia Ramirez (2 года назад)
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 (3 года назад)
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 (3 года назад)
Is it not very similar to Cauchy sequence? I am confused now.. kindly somebody state the difference.
do it annammo (3 года назад)
vry helpful
Joey Ulseth (3 года назад)
Absolutely phenomenal explanations. Thank you so much for the time you put into all of your videos.
Eddie Main (3 года назад)
I like your videos !
Shehan.Seneve (3 года назад)
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 года назад)
Fantastic job explaining.  Kudos!
Maryam A (4 года назад)
AMAZING THANK YOU . wouldve been better if you sequenced your all topology videos in an order . 

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