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!
I think it's possible to compress 00:00 to 03:08 -- "Set M of metric space R is open - if it consisting entirely of interior points" . I think in the previous video you have already covered all details. But in any case - thank you. The vision of such detail can be lie in that this video by itself is self-contained.
open balls are usually written with dotted lines right? I see that you have not used a dotted line for the open ball in the video. Please guide me with this. @Ben1994
awesome video mate but i have a question, what’s stopping us from setting the radius of the epsilon ball to a number big enough so that part of the circle was outside the set meaning that the point was included in an open set?
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.
"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.
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".
The set is open if every point in the set has a neighbourhood within the set itself (for example the interval (0, 1), every x within has a neighbourhood, just pick the lesser between _x_ and _1-x_ (think of it geometrically, a line from 0 to 1 but not including those ones) and set e lesser than min{x, 1-x}. You see that (x-e, x+e) is within (0,1) for an e, foe every x (you can stretch the proof by formalising). A closed set is a set which its complementar is open.
[a, b] is closed since R - [a, b] is open (-inf, b) U (a, inf)= R - [a, b] (-inf, b) is open (a, inf) is open the union of two open sets outcomes another open set
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.)
You definitely should be teaching in a university, you have done a better job than my lecturer, in the scale of 8mins : 2hrs :))
thanks
True
Very informative, concise and intuitive description .10/10 would bang.
This man speaks about sets with a passion.Very helpful video, thanks!
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!
your from which school
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!
I agree Much better than what I learned in class
You are explaining in a clear and easy way for students to understand. Thank you so much!
THANK YOU!
I never understood these before I found your channel
I actually didn't know anything about topology, but now I do. Thanks.
This was always a hole in my background of math at college. Thanks!
I wish you were my Topology professor.
This made sense to me very clearly... Thanks
thank you very much, everything is so clear now
Thanks for giving a good sense of understanding
Amazing class thanks for saving us
please keep doing what you do
Thank you! The pictorial representation makes the difference clearer. :)
great explantion..I irritated my quantum mechanics teacher numerous time yet he couldn't explain this simple concept to me..
Thank you for not confusing me!
I think it's possible to compress 00:00 to 03:08 -- "Set M of metric space R is open - if it consisting entirely of interior points" . I think in the previous video you have already covered all details. But in any case - thank you. The vision of such detail can be lie in that this video by itself is self-contained.
Incredibly helpful, wish you had a series on real analysis
thetedmang He does.
@@ruchikaagarwal5591 He has a topology series, slightly different topic
To the point. Liked and subscribed
thank you good sir!
This so helpful.Thank you so much
Nobody:
Mathematicians: Clopen
SAVED ME! Thank you
Amazing explaination!!
Thank you for watching.
@@elliotnicholson5117 haha...sir i was watching your other videos of metric space
Simple and crisp explaination sir
Great!
Excellent, very clear, thank you
Very good explanation
Thank you, very clear!
In other words, an open set is a set without boundary and all points stay within.
clear explanation, thanks!
Great lecture
great explanation, thank you !
nice explanation. thanks.
is that an electrophorous?
amazing video!
thank you so much
open balls are usually written with dotted lines right? I see that you have not used a dotted line for the open ball in the video. Please guide me with this. @Ben1994
Thankuuu sir ji
awesome video mate but i have a question, what’s stopping us from setting the radius of the epsilon ball to a number big enough so that part of the circle was outside the set meaning that the point was included in an open set?
how do u find closure of an open complex set??
Great!!
Good effort
Great stuff
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....
+Emmeli Skalman hlllllooo
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.
closed bcoz its bounded at -inf and inf
nice video, thanks
You are Intelligent please t
Is the union of intersection of 2 open sets open?
yes
the empty set and the whole space R^n ; are they an open or closed set? The answer? BOTH?!! :(
"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.
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".
I didît understand do u mean it's open set if all elements are in the set U?
And it's closed set if the elements are out of the set C?
The set is open if every point in the set has a neighbourhood within the set itself (for example the interval (0, 1), every x within has a neighbourhood, just pick the lesser between _x_ and _1-x_ (think of it geometrically, a line from 0 to 1 but not including those ones) and set e lesser than min{x, 1-x}. You see that (x-e, x+e) is within (0,1) for an e, foe every x (you can stretch the proof by formalising).
A closed set is a set which its complementar is open.
Thank you .
thanks professer
Open set looks like universe.
it isnt tho
[a, b] is closed since R - [a, b] is open
(-inf, b) U (a, inf)= R - [a, b]
(-inf, b) is open
(a, inf) is open
the union of two open sets outcomes another open set
X is a closed set if the limit of every xn in X (for all n) is in X
What if we work in R+?
wont make a difference, even in R+ infinity is not contained
you are just too good, can you please teach at ubc, fk my prof
good.
Thanks ;)
Who is here from UTEP?
Nigga what?
- an 8th grader who just wants a C in math
what is the difference between open set and open interval? Please reply me 😢
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.)
Toy
The closed set of what you can explain doesn't exist
I was looking for pick up advice lol
No, you weren't studying anything
Too superficial... need proofs steps