Brilliant. There's another lecture series by ben1994 which is extremely longwinded and repetitive, but you've nailed almost an entire series of his in this one video. The best part is that you give topology examples that FAIL as well as those which succeed, which is absolutely vital to reinforce understanding! I'm very impressed, thank you!
I am finishing to study a 5-year degree in Physics, and I want to become the best theoretical physicist I can, focusing my research in the most theoretical and mathematical topics (without converting myself in a mathematician), do you think is necessary to study books of Topology? or is better to focus only on books like differential geometry for physicists, fiber bundles for physicists, knots for physicists, etc.?
Is really necessary the condition "X is not the empty set"? I have studied the definition in several books and I've never seen that explicitly, actually the only major definition in which I remember that explicit condition is that of "model" in logic
I have a couple of questions: 1) how are open sets defined without a metric? 2) what's the difference between a collection and a family (of subsets)? 3) can you make a video on manifolds?
1) by definition, we call the elements of the topology Tau open sets, they are defined by the definition in this video 2) same thing 3) sure, I probably will, I will be posting a lot more stuff on more topics soon I hope:)
note every topology is different, so how open sets are defined depends on the topology, but in general, a topology is just a collection of sets that satisfy certain properties(the ones in this video), and those sets are called open sets. There are so many topologies, all kinds of weird and interesting things. I should make more videos on this too. Long reply sorry, you made me think:)
@@TheMathSorcerer May you make a video with examples of open/close sets of set Y, as a subspace of R. Consider the set Y=[−1,1] as a subspace of ℝ. Which of the following sets are open in Y? Which are open in ℝ? A={x|12
I got question. In example 2, how come last property is not satisfied? I mean, according to property 1, tau is defined by empty set and X and in this example X is consisted of elements of a,b,c. but intersection of {a,b} and {a,c} is equal to {a} which is already in X hence X has element of a,b,c. right?
this was great! I actually understood it! Have you done any more topics related to Intro to topology? I would love to see your explanations. If so, I might actually get through intro to topology!
Here, the “open set” is a general idea in topology. A set is called open, according to Wikipedia, if "the union of an arbitrary number of open sets in the collection is open, the intersection of a finite number of open sets is open". Hence a topology can be both finite and open. For a topology of the real line, however, the open set(or open interval) cannot be finite since it is based on real numbers, but it satisfies the requirements of the general idea of an open set.
@@zanet9259 can you tell me where can i get a brief about open set in topology because the definition you've mentioned is not satisfactory for me as iam new in this.
Awesome as a possum with a blossom!!! I believe I've got topological spaces down pat!! As of the writing of this comment, it is after 11:30 pm PT on June 11, 2019 and I hope I can still remember the workings of this concept tomorrow morning!! LOL!! Thanks lots, Math Sorcerer!!!! :)
I'd tried a little years ago (pre- RUclips) to make sense of topology texts on my own, but this is the first time I've understood even these basic concepts. Very accessible teaching style- thanks!
This is usually done 3rd or 4th year undergraduate in the US. But I think some proof based math is helpful and that should be enough to try to understand it all. It's a cool subject.
@@TheMathSorcerer i am doing first course in real analysis and want to have detailed understanding so i want to take this, i have taken calculus 1 ,2 and basic linear algebra and first course in differential equations, but i have not taken any course like abstract algebra, group theory, ring theory etc. Can i still take this ?
I noticed you switched your definition from the previous video. In this video you have (2) for union and (3) for intersection, but in the previous video it was the other way round. Slightly confusing but I spotted it so will be fine going forward 🙂
Brilliant. There's another lecture series by ben1994 which is extremely longwinded and repetitive, but you've nailed almost an entire series of his in this one video. The best part is that you give topology examples that FAIL as well as those which succeed, which is absolutely vital to reinforce understanding! I'm very impressed, thank you!
Thank you! Your comment is VERY motivating:) These topology videos are very hard to make because it's hard to explain clearly. Thank you thank you!
Finally I get my favourite class and teacher and also channel
😃
X2
Great introduction to point-set topology here,
Thank you😀
I love this! I am trying to understand what a manifold is, and knowing what the term "topological space" means is key!
What does " manifold" mean , I see this expression on many books and I didn't understand it
This alternative definition of a topology makes sense because "open sets" are defined as the elements of Tau in the last video.
I am finishing to study a 5-year degree in Physics, and I want to become
the best theoretical physicist I can, focusing my research in the most
theoretical and mathematical topics (without converting myself in a
mathematician), do you think is necessary to study books of Topology? or
is better to focus only on books like differential geometry for
physicists, fiber bundles for physicists, knots for physicists, etc.?
Good luck 🤞
Any idea on how to self study topology on your own
Yeah the easiest book I have found is free, it's online and it's called topology without tears. It's a beautiful book!
@@TheMathSorcerer I having problems creating my own proof of Ex. 2.2.2(I)
I expect that you will make more videos related to Topology.
Yes I need to!!
Is really necessary the condition "X is not the empty set"? I have studied the definition in several books and I've never seen that explicitly, actually the only major definition in which I remember that explicit condition is that of "model" in logic
I have a couple of questions: 1) how are open sets defined without a metric? 2) what's the difference between a collection and a family (of subsets)? 3) can you make a video on manifolds?
1) by definition, we call the elements of the topology Tau open sets, they are defined by the definition in this video
2) same thing
3) sure, I probably will, I will be posting a lot more stuff on more topics soon I hope:)
note every topology is different, so how open sets are defined depends on the topology, but in general, a topology is just a collection of sets that satisfy certain properties(the ones in this video), and those sets are called open sets. There are so many topologies, all kinds of weird and interesting things. I should make more videos on this too. Long reply sorry, you made me think:)
Why is the capital X set open since it contains three discrete points, a, b and c?
omg, thank you so much for the straight forward toward this topic.
np man
@@TheMathSorcerer May you make a video with examples of open/close sets of set Y, as a subspace of R.
Consider the set Y=[−1,1] as a subspace of ℝ. Which of the following sets are open in Y? Which are open in ℝ?
A={x|12
Good. have you an application of topological space in real life?
Wow ..I love your explanation
Thank you!
I got question. In example 2, how come last property is not satisfied? I mean, according to property 1, tau is defined by empty set and X and in this example X is consisted of elements of a,b,c. but intersection of {a,b} and {a,c} is equal to {a} which is already in X hence X has element of a,b,c. right?
By condition 1 you meant they belong to the topology, not that they are open.
this was great! I actually understood it! Have you done any more topics related to Intro to topology? I would love to see your explanations. If so, I might actually get through intro to topology!
He has a whole playlist of 15 videos on topology! :)
I can see why you notate X with overhead dash and another dash beneath. So the notated X is a non-empty set. Thanks for info.
Its just a notation for capital X, I had a teacher once that would use it so I started using it😄
And if you are curious as to why, well sometimes you have two X's one lowercase and one capital, so the lines really differentiate them
if empty and X sets are not included in tau set.....then they wont be open sets?
that means for a set to be open it must be in topology!
I have an idea for a new video, "induced topology" Thanks
I don't understand how X is open? its a finite set of 3 elements... how is it open?
I had the same question. This will help: mathworld.wolfram.com/OpenSet.html
Here, the “open set” is a general idea in topology. A set is called open, according to Wikipedia, if "the union of an arbitrary number of open sets in the collection is open, the intersection of a finite number of open sets is open". Hence a topology can be both finite and open. For a topology of the real line, however, the open set(or open interval) cannot be finite since it is based on real numbers, but it satisfies the requirements of the general idea of an open set.
@@zanet9259 can you tell me where can i get a brief about open set in topology because the definition you've mentioned is not satisfactory for me as iam new in this.
sir please more class lecture of topology
ruclips.net/video/FV2dmVN_DhI/видео.html
Ok, and whats the practical use of this?
Thank you. This was very helpful. I was a bit confused at first after looking at it again and writing it out I understood.
ruclips.net/video/FV2dmVN_DhI/видео.html
Let X={ all triangles} t={0,X,{right triangles,isocles triangles}}. Is t a topology. If so, how would you show it
Awesome as a possum with a blossom!!! I believe I've got topological spaces down pat!! As of the writing of this comment, it is after 11:30 pm PT on June 11, 2019 and I hope I can still remember the workings of this concept tomorrow morning!! LOL!! Thanks lots, Math Sorcerer!!!! :)
Hehe awesome 😄😄
I'd tried a little years ago (pre- RUclips) to make sense of topology texts on my own, but this is the first time I've understood even these basic concepts. Very accessible teaching style- thanks!
awesome so glad to hear this!
I actually have no idea what you mean by open? Like are those elements inside tau?
What is the prerequisite of this playlist ?
This is usually done 3rd or 4th year undergraduate in the US. But I think some proof based math is helpful and that should be enough to try to understand it all. It's a cool subject.
@@TheMathSorcerer i am doing first course in real analysis and want to have detailed understanding so i want to take this, i have taken calculus 1 ,2 and basic linear algebra and first course in differential equations, but i have not taken any course like abstract algebra, group theory, ring theory etc. Can i still take this ?
@@chandankar5032 sure yes you can...it's hard for some people ..I learned this after taking abstract and linear though
@@chandankar5032 you just have to be decently solid at proof writing..if u can write proofs u got this. But again I learned this after abstract
I’m a with 😟👹🧛🏽♀️🧙🏾
Witch dammit
Thanks sir for this explaintion
Happy it helped 😄
Thanks, super clear.
I noticed you switched your definition from the previous video. In this video you have (2) for union and (3) for intersection, but in the previous video it was the other way round. Slightly confusing but I spotted it so will be fine going forward 🙂
THANK YOU SO MUCH
Very very thankyou sir
Thank you sir,
very happy it helped:)
ruclips.net/video/FV2dmVN_DhI/видео.html
thank you so much sir....for this video.god bless you
np
Prove that all n>=1, πn(S^n) = Z. Sir pls solve this
I actually think I get it.
Thanks!
ruclips.net/video/FV2dmVN_DhI/видео.html
Thank you for this video. Topology is a lot more clear to me now.
+Hayden Hunter Wow thanks, so glad this helped someone:)
Don't know about you, but I find those digital pens have a jumpy, irritating motion and the writing aesthetically ugly.