2022-02-06

22: Continuous, Normed Vectors Spaces Map

<The previous article in this series | The table of contents of this series | The next article in this series>

A definition of continuous, normed vectors spaces map

Topics


About: vectors space

The table of contents of this article


Starting Context



Target Context


  • The reader will have a definition of continuous, normed vectors spaces map.

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 normed vectors spaces, \(V_1\) and \(V_2\), any map, \(f: V_1 \to V_2\), such that for any vector, \(v_{11} \in V_1\), and any vectors sequence, \(v_{1i} \in V_1\), that converges to \(v_{11}\), \(\lim_{v_{1i} \to v_{11}} f (v_{1i}) = f (v_{11})\)


References


<The previous article in this series | The table of contents of this series | The next article in this series>