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Math and science::Topology

Metric space. ε-balls

Let X be a metric space, let xX and let ε>0 be a real. The open ε-ball around x (or in more detail, the open ball around x of radius ε) is the subset of X given by

[ B(x,ε)={yX:what condition?} ]

Similarly, the closed ε-ball around x is

[B¯(x,ε)={yX:what condition?} ]