definition of uniformly continuous map from group with topology with continuous operations (especially, topological group) into normed vectors space with induced topology
Topics
About: group
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of left uniformly continuous map from group with topology with continuous operations (especially, topological group) into normed vectors space with induced topology.
- The reader knows a definition of right uniformly continuous map from group with topology with continuous operations (especially, topological group) into normed vectors space with induced topology.
Target Context
- The reader will have a definition of uniformly continuous map from group with topology with continuous operations (especially, topological group) into normed vectors space with induced topology.
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:
\( G\): \(\in \{\text{ the groups }\}\) with any topology such that the group operations are continuous
\( V\): \(\in \{\text{ the normed vectors spaces }\}\) with the topology induced by the metric induced by the norm
\(*f\): \(: G \to V\)
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Conditions:
\(f \in \{\text{ the left uniformly continuous maps }\} \cap \{\text{ the right uniformly continuous maps }\}\)
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