definition of value-bounded map from set into seminormed vectors space
Topics
About: vectors space
The table of contents of this article
Starting Context
- The reader knows a definition of seminormed vectors space.
- The reader knows a definition of map.
Target Context
- The reader will have a definition of value-bounded map from set into seminormed vectors space.
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:
\( S\): \(\in \{\text{ the sets }\}\)
\( V\): \(\in \{\text{ the seminormed vectors spaces }\}\), with any seminorm, \(\Vert \bullet \Vert\)
\(*f\): \(: S \to V\)
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Conditions:
\(\exists L \in \mathbb{R} (\forall s \in S (\Vert f (s) \Vert \lt L))\)
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2: Note
\(V\) can be a normed vectors space, because any norm is a seminorm.
This concept may be often called "bounded map", but we call this concept "value-bounded map" in order to distinguish this concept from bounded map between normed vectors spaces.
