Let βN be the Stone–Čech compactification of the integers. A point "U" ∈ βN is an ultrafilter on N. A subset "A" ⊆ βN induces a filter "F"("A") = ∩ {"U" : "U" ∈ "A"}. Let b("U", "A") = sup{ inf{ |"n" − "j"| : "n" ∈ "X", "j" ∈ "E" } : "X" ∈ "U", "E" ∈ "F"("A") }. Then (βN, b) is an approach space that extends the ordinary Euclidean distance on N. In contrast, βN is not metrizable.