definition of final map between directed sets
Topics
About: set
The table of contents of this article
Starting Context
- The reader knows a definition of directed set.
Target Context
- The reader will have a definition of final map between directed sets.
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:
\( D_1\): \(\in \{\text{ the directed sets }\}\)
\( D_2\): \(\in \{\text{ the directed sets }\}\)
\(*f\): \(: D_1 \to D_2\)
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Conditions:
\(\forall d_2 \in D_2 (\exists d_1 \in D_1 (\forall s'_1 \in D_1 \text{ such that } d_1 \le s'_1 (d_2 \le f (s'_1))))\)
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