Відео

Why 5:48?

Fj = ∩ i=j to infinity (Ej), you said Fj ⊆ Fj+1 means that it’s an increasing sequence, can you explain how? Because when i am trying to understand its decreasing sequence Fj+1 ⊆ Fj, thanks

Great video :))

Concerning the first exercise: Is Q convex in R? If not, then your counterexample doesn't work, right?

Hi! Thank you for your content, I love your videos they are very neat and organized. I was wondering what software do you use to write them on, if you don't mind.

Thank you.This video is much needed for my exercise.

This is very good lecture, thank you.

I have a question: if fn converges to f pointwisely, if f'n converges to f' pointwisely and if f'n and f' are continuous, then, can we conclude that f'n converges to f' uniformly?

I have a question: if fn converges to f pointwisely, f'n converges to f' pointwisely and if f'n and f' are continuous, then can we conclude that the convergence of f'n to f' is uniform? Thank you in advance.

Hello thank u for your videos..can u provide us with a video about radin measure

Do you know why inner regular is not also defined as open set too? Or not defined as closed set?

For what it's worth I would appreciate more Munkres videos when you've got the time to make them.

Constadinos Caratheodorys , a Greek Mathematician who helped Albert Einstein.

Thanks for the video

can't thank you enough for producing these videos - saved me a LOT of pain this semester! (i don't think i like point-set topology very much 🤣) i think there's a small mistake at 6:30 - i think you mean x_0 \in X and (a,b) i f(x_0), and that you're using a characterization of continuity (Thm 18.1 (4)) currently it's written as x_0 \in [0,1] and (a,b) i x_0, and you state you're using the definition of continuity

thanks for your video. It was helpful

What a great explanation, thanks !

Looking forward to the next videos

6:12 I am really confused why X tilda = Union of Intersection of that set. We also have "for all k", so shouldn't it be equal to Intersection of Union of Intersection of the set?

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Thank you very much for your work here. You would deserve much more views and like! (Maybe only a little more volume at your agreeable voice 😉)

Thank you!

I think the definition of N_r is wrong. It should be the union of two sets which you defined.Not the intersection.

thank you!

hmm, not sure about your proof for R^omega in the box topology - I think we do have to show that B is open. Also, I'm only seeing a theorem in Munkres that X is connected if and only if the only subsets of X that are both open and closed in X are the empty set and X itself, but I think in your video you present it without closed being a necessary condition.

i have a question. G is not a sequence, so what does it mean to say μ(G) --> M?

im wondering if you could perhaps make a video on how to identify the triangle inequality in weird situations and apply it? like an "advanced triangle inequality" video. i struggle with recognizing how to use it when it's not directly identifiable, like in p. 122 or p.125 in this chapter of metric spaces in munkres. thank you! (:

Nice ASMR

great video, once again!! thank you!! it takes me such a long time to read munkres and i feel concerned when i don't understand a small detail; you help me identify and comprehend the main storyline.

i cannot thank you enough for your videos. my professor is extremely unclear, and i find munkres difficult to parse (and am frequently wanting more concrete examples, counterexamples, or images - as an example, i was not sure about what kind of objects his notation represented in his definitions in this section). your videos are a lifesaver in my topology course this fall!!

I don't think the proof for part 1 is correct, you used the same x in two different variables.

Please explain exercises 3.26.1 please help tomorrow is seminar😢

Hola! Pregunta: en el minuto 05:00 ¿no es lo mismo decir que el complemento de tal conjunto B es abierto y eso probaría que B es cerrado? Digo, porque la elección de x0 es arbitraria y siempre vas a poder hallar un abierto Wx que es disjunto de B. Gracias!

I want to thank you about your great videos I found many things that are not found anywhere else only here ❤

We can not take the case Ai's are countable except two uncountable sets A1 and A2 since the measure of the union will still 1 but the sum will be 2 so we must take one uncountable set not two .. ok why ? Is the reasons are the formula of the segma algebra & Ai's are disjoint ? I proved this using contapositive l said let Ai's are countable except two sets A1 and A2 where their completens are countable.. Since Ai's are disjoint then A1 is a subset of the completent of the union of Ai's (with A2) And if we take the complement of each side then we will replace each side I mean the union will be subset of the complement of A1 wich is a contradiction ( uncountable subset of countable is a contradiction)... the union is uncountable since it has A2 which is uncountabl and the complement of A1 is a countable from the formula of the segma algebra ..ok is it a logic reason or proof ? So there exist no case which say Ai's are countable except two ? If yes what about if we take all A are uncountable? .. we will have the same problem What about this case ?

Hi why in proving countable union of measure le set is measurable you suppose the sets are disjoint?

nice

Thank you for the video. I had a question on the first part of the problem. I thought the wording countable implied that we also needed to prove that the basis was a countable one as well. How would you suggest we go about doing that part? Thank you!

Can you please make a video on extension?

Well described , really that brought a clear idea about dictionary order topology. But I am struggling to understand why the dictionary order topology restricted to I=[0,1] is not same as the subspace topology on I×I obtained from the dictionary order topology on R×R...Can you please explain? I can understand that for inherited subspace topology there may be half-open intervals as it is just the intersection of an interval of R×R with the unit square... Is it for like the basis only consists of open intervals for this type of order topology ? Am I right?

Urysohn’s lemma can also be used to prove the Portmanteau theorem.

Sound is very low...thanks

Finally a video where I get the intuition behind how the simple functions are defined. I was never able to understand the intuition till now. Thank you so much!

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in the first question's example...why is Y convex in X??

Very useful video and nicely put together. Gives the viewer a better intuition of the countability axioms by going through an example.

5:45 why it is inf Lim not the opposite Lim inf¿

@ 4:48 when we are considering other case, why are we doing "there exist for some..." when in first case we just start that E_i are countable for all i? Is it just there to eventually force the form (U E_i)^c is countable? Since, in the first case, we already forced (U E_i) is countable by starting all E_i are countable? Proving two case since for something to be in A: (something is subset of X AND something is countable) OR (smthing is subset of X AND smthing-complement is countable} where, in our case, that Something = (U E_i). Lastly, in your video, are we to assume fancy A is subset of Powerset of X? so Since we claimed E in A earlier. E is also subset of X. So union of subsets of X is still subset of X so (U E_i) is subset of X, satisfying first part of each 2 cases? I ask this because I think you only briefly mentioned in the last video fact A is subset of P(X)... sorry for my English.

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