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Introduction to Open and Closed sets

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The concepts of open and closed sets within a metric space are introduced
Категория: Образование
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Текстовые комментарии (44)
Colin McMahon (7 дней назад)
No, you weren't studying anything
Ben Snodgrass (28 дней назад)
Great video very intuitive! however, I still don't see why bringing in the ball of radius epsilon is really necessary - why can't you just say an open set is one that doesn't contain it's boundary and a closed set is one that does? basically just like greater than inequalities as opposed to greater than or equal to inequalities on a one dimensional line
thetedmang (3 месяца назад)
Incredibly helpful, wish you had a series on real analysis
thetedmang (15 дней назад)
+Ruchika Agarwal He has a topology series, slightly different topic
Ruchika Agarwal (15 дней назад)
thetedmang He does.
ekconomos (4 месяца назад)
Very good explanation
Green Scarf (5 месяцев назад)
Your video is very helpful ❤❤❤ thanks a lot
chandin69 (5 месяцев назад)
To the point. Liked and subscribed thank you good sir!
Aabhas Vij (7 месяцев назад)
Is the union of intersection of 2 open sets open?
imran bashir (11 месяцев назад)
Good effort
Harish Kashyap (1 год назад)
amazing video!
Alya Amir (1 год назад)
great explanation, thank you !
Michalis Michaelides (1 год назад)
Thank you .
how do u find closure of an open complex set??
Mr GD (1 год назад)
nice explanation. thanks. is that an electrophorous?
Noah Z. (1 год назад)
please keep doing what you do
sgtcojonez (1 год назад)
I wish you were my Topology professor.
Isaac Wang (1 год назад)
nice video, thanks
Imran Mohammed (2 года назад)
Great lecture
Divyanshi Rastogi (2 года назад)
Thank you! The pictorial representation makes the difference clearer. :)
Rowaida AL-r (2 года назад)
what is the difference between open set and open interval? Please reply me 😢
Thanu Zayaan (19 дней назад)
Darrell McPhail (1 год назад)
An open interval is an open set in the real line, R. An open set in R is not necessarily an interval. It could be the union of several ('countably' many) open intervals, for example. To talk about 'openness' you need to specify the base set. An interval that is open in R is neither open nor closed in the Euclidean plane (for example.)
이건희 (2 года назад)
thanks professer
Thomas Edison (2 года назад)
Thanks ;)
石崴 (2 года назад)
clear explanation, thanks!
adankey 0_0 (2 года назад)
I was looking for pick up advice lol
Emmeli Skalman (2 года назад)
what about if i just have a straight line like {(x,y): 4x+3y=7}, is that open or closed or nether? i mean, it goes from -infinity to infinity....
Corlin Fardal (2 года назад)
It's closed. If you consider it's complement you'll see that no matter how close the points get to the line, there will always exist an open ball, meaning that the complement is open, so the line is closed.
Abid 111 (2 года назад)
+Emmeli Skalman hlllllooo
Kid Buu (2 года назад)
"closed is complement of open" It is not true. While you paint the plane in blue you didnt draw the boundary line of the plane, thats implying the plane you drew, is an open plane. It is open one side but closed on other side.
Corlin Fardal (2 года назад)
No, under any topology course I have seen, the definition of a closed set is ALWAYS the complement of an open set. The "open plane" doesn't have anything to do with it because the plane in provably both open and closed, so you could say it's actually closed "from all sides".
ABHINANDAN DASS (2 года назад)
great explantion..I irritated my quantum mechanics teacher numerous time yet he couldn't explain this simple concept to me..
buddahratt shojobo (2 года назад)
Very informative, concise and intuitive description .10/10 would bang.
Joel Castellon (2 года назад)
This was always a hole in my background of math at college. Thanks!
Alexander Lewzey (2 года назад)
Great stuff
Pete Fitton (3 года назад)
Excellent, very clear, thank you
Cross Tran (3 года назад)
You definitely should be teaching in a university, you have done a better job than my lecturer, in the scale of 8mins : 2hrs :)) thanks
Priyabrata Senapati (3 года назад)
Hassan Al-Saadi (3 года назад)
Thanks, it is very clear.
Usman Bashir (3 года назад)
Great and succinct. Found this vid after about an hour of struggling with various other resources online and understand the concept in 8 minutes. Cheerios!
jadoreux (3 года назад)
Less than 2 minutes in and my question is answered straight away! Just needed the definition I guess but was never given it, thank you!
martin kioko (1 год назад)
your from which school
bexisbonkers (3 года назад)
Thank you for not confusing me!

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