in a topological space
An element of the topology (cf. Topological structure (topology)) of this space. More specifically, let the topology of a topological space be defined as a system of subsets of the set such that: 1) , ; 2) if , , then ; and 3) if , , then . The open sets in the space are then the elements of the topology and only them.
|[a1]||R. Engelking, "General topology" , Heldermann (1989)|
Open set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Open_set&oldid=18168