definition of map between topological spaces locally homeomorphic at point
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of homeomorphism.
Target Context
- The reader will have a definition of map between topological spaces locally homeomorphic 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:
\( T_1\): \(\in \{\text{ the topological spaces }\}\)
\( T_2\): \(\in \{\text{ the topological spaces }\}\)
\( t\): \(\in T_1\)
\(*f\): \(: T_1 \to T_2\)
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Conditions:
\(\exists U_t \subseteq T_1 \in \{\text{ the open neighborhoods of } t\}, \exists U_{f (t)} \subseteq T_2 \in \{\text{ the open neighborhoods of } f (t)\} (f \vert_{U_t}: U_t \to U_{f (t)} \in \{\text{ the homeomorphisms }\})\)
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