Most commonly we use as basis to generate the standard topology on Rn the set of all open balls, what would be an example of a second-countable basis that still suffices to generate a topology on Rn?
You can define balls using the 2n norm, or take the infinity norm which gives you open "squares". Alternatively, take the standard topology on R and extend to the product topology on R^n.
that is an atrocious comment to make. i sincerely request that you take a good solid look in the mirror and ask yourself how you could possibly muster up the courage to say such things about such a beautiful man. i demand that you apologise. now.
@@karm00n29 in what world is muscle mass directly related to health? bold of you to assume that he isn’t healthy coz he’s lean, there is no science to back that.
Exciting video. Great board drawings--I feel like I'm watching Frederic Schuller
That's quite a compliment. I'm familiar with Schuller's lectures also, and QN3 does a great job approximating Frederic.
Excellent explanation, I appreciate your work a lot
holy moly 😍😍
Exciting video, looking forward for following parts. Happy holidays, everyone.🎊
Hype!
Welcome back professor
Thanks for the material 😏
Brilliant
Thank you for this video!
Very excited for this topic series! What are the pre-requisites before watching this series?
Some topology, multivariable calculus, and linear algebra
Not sure if the manifolds or QnCubed3 is more beautiful!
you are
Most commonly we use as basis to generate the standard topology on Rn the set of all open balls, what would be an example of a second-countable basis that still suffices to generate a topology on Rn?
You can define balls using the 2n norm, or take the infinity norm which gives you open "squares". Alternatively, take the standard topology on R and extend to the product topology on R^n.
@@qncubed3 Thank you very much! 0) with the range of the centres limited only to the rationals in order to make them countable.
Will you marry me?
I will
Are you good at maths?
@@wealllovelain not in pure,but somewhat better in applied
@@quonxinquonyi8570 Good enough for me, here’s your ring 💍
Good enough for me, here’s your ring 💍
hey man youre smart as hell, but you should try hitting the gym
I'll write with my legs next time :)
i love your confidence with that profile pic! don’t do it again
that is an atrocious comment to make. i sincerely request that you take a good solid look in the mirror and ask yourself how you could possibly muster up the courage to say such things about such a beautiful man. i demand that you apologise. now.
I am 100% serious lads, the man needs to put on some muscle. Stronger body - stronger mind, also, longer life expentancy for fitter people
@@karm00n29 in what world is muscle mass directly related to health? bold of you to assume that he isn’t healthy coz he’s lean, there is no science to back that.