A definition of map continuous at point
Topics
About: topological space
The table of contents of this article
Starting Context
- The reader knows a definition of topological space.
- The reader knows a definition of map.
Target Context
- The reader will have a definition of 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: Definition
For any topological spaces, \(T_1\) and \(T_2\), and any point, \(p \in T_1\), any map, \(f: T_1 \to T_2\), such that for any neighborhood, \(U_{f (p)}\), of \(f (p)\), there is a neighborhood, \(U_p\), of \(p\) such that \(f (U_p) \subseteq U_{f (p)}\)
