Definition:Diagonal Relation/Also known as
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Diagonal Relation: Also known as
The diagonal relation can also be referred to as:
- the equality relation or relation of equality
- the identity relation.
It is also referred to it as:
- the diagonal set or diagonal class
- the diagonal subset or diagonal subclass.
Some sources call it just the diagonal.
However, $\mathsf{Pr} \infty \mathsf{fWiki}$'s position is that it can be useful to retain the emphasis that it is indeed a relation.
Sources
- 1955: John L. Kelley: General Topology ... (previous) ... (next): Chapter $0$: Relations
- 1960: Paul R. Halmos: Naive Set Theory ... (previous) ... (next): $\S 7$: Relations
- 1964: Steven A. Gaal: Point Set Topology ... (previous) ... (next): Introduction to Set Theory: $1$. Elementary Operations on Sets
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 5$: Composites and Inverses of Functions
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 4$. Relations; functional relations; mappings: Example $4.2$
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces: Uniformities