Thanks for providing these video. I have learned many thing from these. This course contained two part of topology, general (or point set) topology and algebraic topology, but most of these lectures are about general topology, from lecture 1 to lecture 15. I have concluded the topics of these lectures from 1 to 15 : Lecture 1 Introduction, the definition of topology and basis Lecture 2 sub-basis, order topology and product topology Lecture 3 subspace, closed set, limit point and Hausdorff space Lecture 4 more Hausdorff space, continuous function and homeomorphsim Lecture 5 the properties of continuous function, product topology and box topology Lecture 6 metric topology, metrizable space and uniform topology Lecture 7 sequence lemma and its application Lecture 8 first countable, quotient map and connected topological space Lecture 9 linear continuous, intermediate value theorem and path connected Lecture 10 locally connected, component and compact space Lecture 11 the properties of compact space and the min-max value theorem Lecture 12 limit point compact, sequentially compact and countability Lecture 13 more countability and the separation axioms Lecture 14 more separation axioms and the Urysohn lemma Lecture 15 the Urysohn metrizable theorem The last 5 lectures are about the fundamental group and covering spaces, which are parts of algebraic topology. I have not learned for some personal reasons. the textbook is TOPOLOGY: A FIRST COURSE by J.R. Munkres. Thanks a lot!
you can check the ictp tv website to watch the second part entitled by algebraic topology ( i think they do not uploaded here yet). there you can download any lecture and i think is more organized. acess www.ictp.tv
im 1/3 of the way of the abstract algebra course be benedict gross. once im left with 4-5 lectures. Ill start this. so that i can finally start algebraic topology.
Different student, different background. I haven't learned it, so I do not know the proof for your theorem. The DeMorgan's is useful for students coming from set theory backgrounds.
17:20 Help me understand. In this system ⊂ means "is a subset of" (equality included) So one of the definitions he gives is necessarily false. I assume " T is finer than T' if T contains more subsets than T' " .... is false. yes? T and T' may be perfectly identical, and in this case both mutually coarser and finer than each other. Fine. But if they are identical, one does not contain more subsets than they other. The correct statement is "T is STRICTLY finer than T' if T contains MORE subsets than T' ".... yes? Or are we redefining "more" to mean "more or maybe the same"?
No, it is "T is finer than T' if T is equal or contains more subsets than T' ". You yourself said that you included equality. I don't know what you don't understand ?
I'm confused, @56:42 where we prove the union of all U_a sets is open, how do we start with the assumption "Let x in Union U_a, where a in J, is open"? Are we just trying to show that the family B is a subset of U?
@@sashaallan855 We want to prove that with a set X, subsets U_a and a basis, we have a corresponding topology T. So he tries to prove the 3 conditions for a topology. Here he is trying to prove the 2nd condition that arbitrary unions of U_a are open. So given an element x in the arbitrary union of U_a and a basis, the union is open if there exist a basis element B contained in the arbitrary union of U_a.
So we need to prove that arbitrary unions of U in T can also have all their x contained by basis elements B_x. This is trivial : We take a point x in Union U_a. Then x must be in at least one of the U_a. As all U_a can have their x contained by basis elements, then x, which is in one of the U_a, has a basis element which contains it.
in 41:29, he said about collection (family). Does he mean that collection is the same as multiset since he said in set each element appears once and each element in collection may appear infinite number of times
Yeaa haha you need to do loqer courses sorry sir * Ai bun etin uni ene Gedrata wela potk balan 🤣 Me kibwal krnada😂 Bank ahnko X ooo this is topology did you understand🙄
He assumes you already know everything before the class. This is why many people lose interest in certain topics in math. ‘Make it fun, use real examples, explain everything you use.
To be honest what he is assuming is not that much, and plus he at least acknowledged that students question and didn't ignore it like many professors do.
Well, in Italy at the mathematics university course you start talking seriously about topology at the third year, in GEOMETRIA 3, so it is fair to ask for a pretty deep knowledge in differential geometria and advanced algebra before doing this topic and understand it with no problems
Thmnge baswen mnisummta dna de kiyan prduweyan kibo 😑 Esela eka more genral thige labe symbol ekta wada😑 Proof eka puae ghan wadiweyan B topolgy thrunda dan thota bruni 🤣
Thanks for providing these video. I have learned many thing from these. This course contained two part of topology, general (or point set) topology and algebraic topology, but most of these lectures are about general topology, from lecture 1 to lecture 15. I have concluded the topics of these lectures from 1 to 15 :
Lecture 1 Introduction, the definition of topology and basis
Lecture 2 sub-basis, order topology and product topology
Lecture 3 subspace, closed set, limit point and Hausdorff space
Lecture 4 more Hausdorff space, continuous function and homeomorphsim
Lecture 5 the properties of continuous function, product topology and box topology
Lecture 6 metric topology, metrizable space and uniform topology
Lecture 7 sequence lemma and its application
Lecture 8 first countable, quotient map and connected topological space
Lecture 9 linear continuous, intermediate value theorem and path connected
Lecture 10 locally connected, component and compact space
Lecture 11 the properties of compact space and the min-max value theorem
Lecture 12 limit point compact, sequentially compact and countability
Lecture 13 more countability and the separation axioms
Lecture 14 more separation axioms and the Urysohn lemma
Lecture 15 the Urysohn metrizable theorem
The last 5 lectures are about the fundamental group and covering spaces, which are parts of algebraic topology. I have not learned for some personal reasons.
the textbook is TOPOLOGY: A FIRST COURSE by J.R. Munkres.
Thanks a lot!
You are a hero
A real hero
you can check the ictp tv website to watch the second part entitled by algebraic topology ( i think they do not uploaded here yet). there you can download any lecture and i think is more organized.
acess www.ictp.tv
@@pedrohbb123 Thanks for your recommendation 😊.
@@pedrohbb123 TKS!
Mankres Topology: A First course
is a very outstanding reference for general topology.
It would be great to have specified in the description of each video the topics covered in the lecture
la flaca if you go on Zimmermanns official site you will find the entire program of Geometry 1 and Geometry 3 (Topology)
@@StefSubZero270 can you give me the link please...
@@iamlrk just type "Bruno Zimmermann UniTS" on google and you get it
@@StefSubZero270 oh, I had just typed just Bruno Zimmerman and got a fashion website 😅😅… thanks got it...
When you're googling a mathematician, adding "math" after their name really helps
Thanks for this educational contribution.
im 1/3 of the way of the abstract algebra course be benedict gross. once im left with 4-5 lectures. Ill start this. so that i can finally start algebraic topology.
We don't need DeMorgans at 24:09 to show that arbitrary union of cofinite sets is cofinite, as any superset of a cofinite set is cofinite 🤷🏽♂️
Different student, different background. I haven't learned it, so I do not know the proof for your theorem. The DeMorgan's is useful for students coming from set theory backgrounds.
My question is does the fund trade at NAV or does it fluctuate between at a premium or at a discount to NAV.
This course is absolutely the first course about the general topology. However, it may pay more attention on the metrizability of a topological space.
I like this guy
17:20 Help me understand.
In this system ⊂ means "is a subset of" (equality included)
So one of the definitions he gives is necessarily false.
I assume " T is finer than T' if T contains more subsets than T' " .... is false. yes?
T and T' may be perfectly identical, and in this case both mutually coarser and finer than each other. Fine.
But if they are identical, one does not contain more subsets than they other.
The correct statement is "T is STRICTLY finer than T' if T contains MORE subsets than T' ".... yes?
Or are we redefining "more" to mean "more or maybe the same"?
No, it is "T is finer than T' if T is equal or contains more subsets than T' ".
You yourself said that you included equality. I don't know what you don't understand ?
Where are the other lectures? I cant find them!
Donlans Donlans search using google under Bruno Zimmerman and you can see all 20 lectures..
Nice course no need to do topology
Again.
Kellwema yawna.
"Intersezioni finiti"
Cit
I WANT TO BUY THE PROFESSOR'S BOOK.
Does anyone know which exercises to work with for this class?
From Munkres topology may be
I'm confused, @56:42 where we prove the union of all U_a sets is open, how do we start with the assumption "Let x in Union U_a, where a in J, is open"? Are we just trying to show that the family B is a subset of U?
.
@@sashaallan855 We want to prove that with a set X, subsets U_a and a basis, we have a corresponding topology T. So he tries to prove the 3 conditions for a topology. Here he is trying to prove the 2nd condition that arbitrary unions of U_a are open. So given an element x in the arbitrary union of U_a and a basis, the union is open if there exist a basis element B contained in the arbitrary union of U_a.
So we need to prove that arbitrary unions of U in T can also have all their x contained by basis elements B_x. This is trivial :
We take a point x in Union U_a.
Then x must be in at least one of the U_a.
As all U_a can have their x contained by basis elements, then x, which is in one of the U_a, has a basis element which contains it.
Is this possible to get course outline of this course?
what chapters of munkres does the lecture series follow?
2,3,4 and 9 I think
DISUGULIANZA TVIANGOLAVE!!!!!!!!! cit.
35:00 Surprised by students got tangled by different notations.
in 41:29, he said about collection (family). Does he mean that collection is the same as multiset since he said in set each element appears once and each element in collection may appear infinite number of times
A family is usually just a set of sets. There is no notion of elements appearing multiple times in a family in this context.
What is ICTP?
Yeaa you kow
Z
This is topology eyaaa mor generla 😏
Yeaa haha you need to do loqer courses sorry sir
*
Ai bun etin uni ene
Gedrata wela potk balan 🤣
Me kibwal krnada😂
Bank ahnko
X ooo this is topology did you understand🙄
I really find more useful the relative notation of a complementary set... It's not a matter of taste...
Complement is stupid nothing we have say from where you take difference that's why he use it. There is nothing called universal set
@@sathasivamk1708 The "c" notation can be used when the context is unambiguous. There is no concept of universal set involved.
Bruh can you not write in cartinese...
Baswaen
Edinwda habena dein
Topology calls ekta matemtical proof eka gena ekia
Wadda bruno mali.
1:24:25
35：00想用结论证结论，lol
he was not aware that the two complement notations are same thing.Preliminary set theory needed.
Bana ahapn 1k wakd na.
Nikan symbol liyane ape ewal iyath ba bun 😂
Mewa hodaii athel ekta thiyen atgel ekta🤣
Ema tham dan stat neelan ene😂
Ekta yandi mekt dnew pars🤣
For all gwata wakd name topologistaltaeka trhe na😑
Ewa denaekta dnewa ecrai😒
Amith eka mrneda🤣
Anika moda hiruni ema ekiyakuth lnakwe newa. 🤣
Mewa ma ugan eka hodi etin sthel ekata😑
Moka me uni eka😕
Apitnum etawada genrally egnuwaki.
Donut eka arn kpala penal🤣
More genral
Dan de mnisumta kiya egena ganin balo 😑
Etkotai wtine
Watiam dnumak wene
Natnum kamreta wela proof krla kta piyan edan 😑
Anith un komda dne thi proof kalda nda😒
It says a lot when there is no Chinese / Indian in the class.
I was wondering the same XD
What does it say
It's in Italy guys...
It says nothing
It say you are a bitch lol
He assumes you already know everything before the class. This is why many people lose interest in certain topics in math. ‘Make it fun, use real examples, explain everything you use.
To be honest what he is assuming is not that much, and plus he at least acknowledged that students question and didn't ignore it like many professors do.
Basic set theory is not hard to learn
Theking Ofghana I find him so dull, he seems bored himself...
It's not engineering course lol
Well, in Italy at the mathematics university course you start talking seriously about topology at the third year, in GEOMETRIA 3, so it is fair to ask for a pretty deep knowledge in differential geometria and advanced algebra before doing this topic and understand it with no problems
Bruno mali ban ahapan 😑
Thmnge baswen mnisummta dna de kiyan prduweyan kibo 😑
Esela eka more genral thige labe symbol ekta wada😑
Proof eka puae ghan wadiweyan
B topolgy thrunda dan thota bruni 🤣
Why would anybody pay to listen to this?