Yay! I never took a topology course for my math major at university and only learned some basic topology concepts for some other classes. I’ve enjoyed your real and complex analysis videos too so I’m excited for this series.
At 7:42, you've set delta to potentially be x-a. If that's the case, haven't you created a radius around x that INCLUDES a? I expected you to set delta to be for instance HALF the minimum of x-a and b-x. That way, the sub-interval around x would never approach either endpoint.
We've got a radius that comes right up to a, but the interval we're creating is an open interval, so it doesn't include a. Also, our definition only requires that we find an open interval that's a subset; it doesn't have to be a proper subset. So it's fine that the one we find for 1/2 in (0,1) is (0,1) itself, and generally that we're finding intervals that are lined up on at least one side.
I took a topology course in 1988 and only sort of got it so I'll be interested in what you end up covering in this course Glad to see you've also made a video on Heine Borel.
Ohhhh, nice! Finally, topology! Hopefully some algebraic topology with homologies and homotopies will be covered too. So grateful you are finally making the course!
It's strange to me that you "define" the elements of T as "open sets" alluding to the previous definition of "open set" but without proving that the definition properties imply that all those elements are indeed open in the first sense. I was expecting that you showed that conditions 1, 2, and 3 imply that all sets U in T are necessarily open in the original sense. Or for example if X is the real numbers, then we recover the previous definition of open intervals.
Yay! I never took a topology course for my math major at university and only learned some basic topology concepts for some other classes. I’ve enjoyed your real and complex analysis videos too so I’m excited for this series.
Where is the real analysis videos? I can't find it.
@ it’s on his main channel Michael Penn
@@zachedwards5911 thanks.
Soo happy you're making a topology series
Just finishing up your Lie Algebra series, looking forward to this as well!
Great start to the new series.
I’m psyched! 😀
Didn’t expect this!!! I’m still looking forward to a Galois theory series though 😅😅
So excited. I’ve been waiting for this for so long!!
I've been waiting for a topology course! I wanted to pick up my self study of the topic again to eventually return for my masters.
Yay! new course!
Would love for you to get to algebraic topology eventually!
At 7:42, you've set delta to potentially be x-a. If that's the case, haven't you created a radius around x that INCLUDES a?
I expected you to set delta to be for instance HALF the minimum of x-a and b-x. That way, the sub-interval around x would never approach either endpoint.
We've got a radius that comes right up to a, but the interval we're creating is an open interval, so it doesn't include a. Also, our definition only requires that we find an open interval that's a subset; it doesn't have to be a proper subset. So it's fine that the one we find for 1/2 in (0,1) is (0,1) itself, and generally that we're finding intervals that are lined up on at least one side.
LET'S GOOOO TOPOLOGY COURSE
I took a topology course in 1988 and only sort of got it so I'll be interested in what you end up covering in this course
Glad to see you've also made a video on Heine Borel.
Rock on Michael!
Awesome. I love topology.
Hell yeah new course
I am watching this with two days left until the final exam in my topology class. 😂
Yooo how'd you do?
@@sweetdannyandlisa6537 I got like 80%, but I am satisfied with the result because I was really struggling with that class.
@@sweetdannyandlisa6537 I got like 80% on the exam, but I am pretty satisfied with it because I was really struggling in that class.
@sweetdannyandlisa6537 I got like 80%, but I am satisfied with it because I was really struggling in that class.
@@danielpark9033 hey, 80% is a good grade, no? Congratulations, man
Please update the differential equations playlist. You guys have uploaded 48 vids but there are only 30 there
finally topology :)
My gyad.. its finally here🤩
So you define +oo as oo. I was taught that the symbol oo is the open set (-oo, +oo)
Huh, I’ve never seen that before. I like to just use ℝ instead of writing out the interval (-∞, ∞)
Ohhhh, nice! Finally, topology! Hopefully some algebraic topology with homologies and homotopies will be covered too. So grateful you are finally making the course!
Oh yes
It's strange to me that you "define" the elements of T as "open sets" alluding to the previous definition of "open set" but without proving that the definition properties imply that all those elements are indeed open in the first sense.
I was expecting that you showed that conditions 1, 2, and 3 imply that all sets U in T are necessarily open in the original sense. Or for example if X is the real numbers, then we recover the previous definition of open intervals.
are you following any textbook?
Extreme need Plz quickly complete that