definition of uniformly continuous map between metric spaces
Topics
About: metric space
The table of contents of this article
Starting Context
- The reader knows a definition of metric space.
Target Context
- The reader will have a definition of uniformly continuous map between metric spaces.
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:
\( M_1\): \(\in \{\text{ the metric spaces }\}\)
\( M_2\): \(\in \{\text{ the metric spaces }\}\)
\(*f\): \(: M_1 \to M_2\)
//
Conditions:
\(\forall \epsilon \in \mathbb{R} \text{ such that } 0 \lt \epsilon (\exists \delta \in \mathbb{R} \text{ such that } 0 \lt \delta (\forall m_1 \in M_1 (f (B_{m_1, \delta}) \subseteq B_{f (m_1), \epsilon})))\)
//
2: Note
The point is that \(\delta\) does not depend on \(m_1\).
