Question

what is open ball and what is open set?

Answer 1

open ball:If (M, d) is a metric space, an open ball is a set of the form B(x; r) := {y in M : d(x, y) < r}, where x is in M and r is a positive real number, the radius of the ball. An open ball of radius r is an open r-ball. Every open ball is an open set in the topology on M induced by d.

Answer 2

open set: An open set is a member of the topology.

Answer 3

what is meant by "Every open ball is an open set" means open ball and open set is same?

Answer 4

can u explain it with the help of an example?