Metric space
Open ball
In any metric space (𝑋,𝑑), we can define the open ball of radius 𝑟 around a point 𝑎
B𝑟(𝑎)={𝑥∈𝑋:𝑑(𝑥,𝑎)<𝑟}
where 𝑎 ∈𝑋, and naturally 𝑟 ∈ℝ+. #m/def/anal
The open balls form the topological basis for a Metric topology.
#state/tidy | #lang/en | #SemBr