Editing Net (mathematics) (section)

{{Short description|A generalization of a sequence of points}}
{{About|nets in topological spaces|unfoldings of polyhedra|Net (polyhedron)}}
{{Use dmy dates|date=December 2024}}

In mathematics, more specifically in [[general topology]] and related branches, a '''net''' or '''Moore–Smith sequence''' is a [[Function (mathematics)|function]] whose domain is a [[directed set]]. The [[codomain]] of this function is usually some [[topological space]]. Nets directly generalize the concept of a [[sequence]] in a [[metric space]]. Nets are primarily used in the fields of [[Mathematical analysis|analysis]] and [[topology]], where they are used to characterize many important [[Topological property|topological properties]] that (in general), sequences are unable to characterize (this shortcoming of sequences motivated the study of [[sequential space]]s and [[Fréchet–Urysohn space]]s). Nets are in one-to-one correspondence with [[Filter (mathematics)|filters]].