definition of metric spaces map continuous at point
Topics
About: metric space
The table of contents of this article
Starting Context
- The reader knows a definition of metric space.
- The reader knows a definition of map.
- The reader knows a definition of open ball around point on metric space.
Target Context
- The reader will have a definition of metric spaces map continuous at point.
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:
\( M_1\): \(\in \{\text{ the metric spaces }\}\)
\( M_2\): \(\in \{\text{ the metric spaces }\}\)
\( m\): \(\in M_1\)
\(*f\): \(: M_1 \to M_2\)
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Conditions:
\(\forall \epsilon \in \mathbb{R} \text{ such that } 0 \lt \epsilon (\exists \delta \in \mathbb{R} \text{ such that } 0 \lt \delta (f (B_{m, \delta}) \subseteq B_{f (m), \epsilon}))\)
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