Editing Open set (section)

=== Metric space ===
A subset ''U'' of a [[metric space]] {{math|(''M'', ''d'')}} is called ''open'' if, for any point ''x'' in ''U'', there exists a real number ''ε'' > 0 such that any point <math>y \in M</math> satisfying {{math|''d''(''x'', ''y'') < ''ε''}} belongs to ''U''. Equivalently, ''U'' is open if every point in ''U'' has a neighborhood contained in ''U''.

This generalizes the Euclidean space example, since Euclidean space with the Euclidean distance is a metric space.