A definition of subnet of net with directed index set
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of net with directed index set.
- The reader knows a definition of final map between directed sets.
Target Context
- The reader will have a definition of subnet of net with directed index 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, \(S_1\), any topological space, \(T\), and any net with directed index set, \(f_1: S_1 \rightarrow T\), any net with directed index set, \(f_1 \circ f_2: S_2 \rightarrow T\) where \(S_2\) is any directed set and \(f_2: S_2 \rightarrow S_1\) is any final map between directed sets
