Definition:Mapping/Diagrammatic Presentations/Infinite
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Diagrammatic Presentation of Mapping on Infinite Set
The following diagram illustrates the mapping:
- $f: S \to T$
where $S$ and $T$ are areas of the the plane, each containing an infinite number of points.
Note that by Image is Subset of Codomain:
- $\Img f \subseteq \Cdm f$
There are no other such constraints upon the domain, image and codomain.
Sources
- 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): $\S 1.3$
- 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 3.1$. Mappings
- 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 0.4$
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Functions
- 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions