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: Structured Description
Here is the rules of Structured Description.
Entities:
\( D_2\): \(\in \{\text{ the directed sets }\}\)
\( T\): \(\in \{\text{ the topological spaces }\}\)
\( f_2\): \(: D_2 \to T\)
\( D_1\): \(\in \{\text{ the directed sets }\}\)
\( f_1\): \(: D_1 \to D_2\), \(\in \{\text{ the final maps }\}\)
\(*f_2 \circ f_1\): \(: D_1 \to T\)
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Conditions:
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\(f_2 \circ f_1\) is called "subnet of \(f_2\)".
