Gleason's theorem

In mathematics, the ε-neighborhood (or epsilon-neighborhood) of a set A ⊆ M, where (M, d) is a metric space, is the set of all points of M whose distance to some point of A is less than ε > 0. It is customarily denoted by A^ε. One may write

$A^{\varepsilon }:=\{p\in M|\exists q\in A\mathrm {\,s.t.\,} d(p,q)<\varepsilon \}=\bigcup _{p\in A}B_{\varepsilon }(p)$

where B_ε(p) is the open ball of radius ε centered at a point p of M.

References

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