A definition of net with directed indices set
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of directed set.
- The reader knows a definition of topological space.
- The reader knows a definition of map.
Target Context
- The reader will have a definition of net with directed indices set.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For any directed set, \(S\), and any topological space, \(T\), any map, \(f: S \to T\)
2: Note
Any sequence on any topological space is a net with directed indices set, because the natural numbers set (whether it includes \(0\) or not) is a directed indices set and the sequence is a map from the natural numbers set into the topological space.
