definition of continuous, normed vectors spaces map
Topics
About: vectors space
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of normed vectors spaces map continuous at point.
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: Structured Description
Here is the rules of Structured Description.
Entities:
\( F_1\): \(\in \{\mathbb{R}, \mathbb{C}\}\), with the canonical field structure
\( F_2\): \(\in \{\mathbb{R}, \mathbb{C}\}\), with the canonical field structure
\( V_1\): \(\in \{\text{ the normed vectors spaces over } F_1\}\)
\( V_2\): \(\in \{\text{ the normed vectors spaces over } F_2\}\)
\(*f\): \(: V_1 \to V_2\)
//
Conditions:
\(\forall p \in V_1 (f \in \{\text{ the maps from } V_1 \text{ to } V_2 \text{ continuous at } p\})\)
//
2: Natural Language Description
For \(\mathbb{R}\) or \(\mathbb{C}\) with the canonical field structure, \(F_1\), \(\mathbb{R}\) or \(\mathbb{C}\) with the canonical field structure, \(F_2\), any normed vectors space over \(F_1\), \(V_1\), and any normed vectors space over \(F_2\), \(V_2\), any map, \(f: V_1 \to V_2\), such that for each \(p \in V_1\), \(f\) is continuous at \(p\)
