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+. anal The open balls form the topological basis for a Metric topology.

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