Open sets of real numbers -- Topology video 1

[@jsham92]

Soo happy you're making a topology series

[@zachedwards5911]

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.

[@alpercay3941]

Where is the real analysis videos? I can't find it.

[@GhostyOcean]

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.

[@saadmollaei1769]

Yay! new course!

[@ra-hu3lu]

Hell yeah new course

[@Yakushii]

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.

[@iabervon]

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.

[@riact123]

Just finishing up your Lie Algebra series, looking forward to this as well!

[@Alan-zf2tt]

Rock on Michael!

[@ScouseRobert]

Great start to the new series. I’m psyched! 😀

[@yuseifudo6075]

LET'S GOOOO TOPOLOGY COURSE

[@Happy_Abe]

Would love for you to get to algebraic topology eventually!

[@hxc7273]

Awesome. I love topology.

[@abdurrahmanlabib916]

Please update the differential equations playlist. You guys have uploaded 48 vids but there are only 30 there

[@harryh5666]

My gyad.. its finally here🤩

[@danielpark9033]

I am watching this with two days left until the final exam in my topology class. 😂

[@bennoarchimboldi6245]

Didn’t expect this!!! I’m still looking forward to a Galois theory series though 😅😅

[@GugasSoares]

are you following any textbook?

[@pseudolullus]

Oh yes

[@gp-ht7ug]

So you define +oo as oo. I was taught that the symbol oo is the open set (-oo, +oo)

[@redpepper74]

Huh, I’ve never seen that before. I like to just use ℝ instead of writing out the interval (-∞, ∞)

[@radadadadee]

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.

[@AntoshaPushkin]

Ohhhh, nice! Finally, topology! Hopefully some algebraic topology with homologies and homotopies will be covered too. So grateful you are finally making the course!

[@happy.5]

Extreme need Plz quickly complete that