definition of net with directed index set eventually in subset
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 net with directed index set eventually in subset.
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: Structured Description
Here is the rules of Structured Description.
Entities:
\( D\): \(\in \{\text{ the directed sets }\}\)
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( S\): \(\subseteq T\)
\(*f\): \(: D \to T\)
//
Conditions:
\(\exists d \in D (\forall d' \in D \text{ such that } d \le d' (f (d') \in S))\)
//
\(f\) is called "eventually in \(S\)".
