Editing Net (mathematics) (section)

===Other properties===

In general, a net in a space <math>X</math> can have more than one limit, but if <math>X</math> is a [[Hausdorff space]], the limit of a net, if it exists, is unique. Conversely, if <math>X</math> is not Hausdorff, then there exists a net on <math>X</math> with two distinct limits.  Thus the uniqueness of the limit is {{em|equivalent}} to the Hausdorff condition on the space, and indeed this may be taken as the definition.  This result depends on the directedness condition; a set indexed by a general [[preorder]] or [[partial order]] may have distinct limit points even in a Hausdorff space.