Question

an open ball is also an open set but can an open set is also an open ball?

Answer 1

let (a,b) be an open set in R, such that a<b,
B((a+b)/2; (b-a)/2)
I am not sure ... just an observation.

Answer 2

please explain that how can this be the ans of "an open set is also an open ball or not"?

Answer 3

of course I created an open ball of center of (a+b)/2 and radius (b-a)/2

Answer 4

*note: I myself is just a beginner. I have high probability of being wrong.

Answer 5

a chuiuiuiua can is also a dog; can a dog be a chuiuiuiua?

Answer 6

yo quiero taco bell lol

Answer 7

You can create an open ball in an open set. That's how many prove that the set is open.You create a ball with radius r and then show that any interior point in the (open) set is less than the distance r.