A definition of accumulation value 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.
Target Context
- The reader will have a definition of accumulation value 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, \(S\), any topological space, \(T\), and any net with directed index set, \(f: S \rightarrow T\), any point, \(p \in T\), such that for any neighborhood, \(N_p \subseteq T\), of \(p\) and any index \(i_0 \in S\), there is an index, \(i \in S\), such that \(i_0 \leq i\) and \(f (i) \in N_p\)
2: Note
A net with directed index set can have multiple accumulation values.
