Projection (set theory)
From Wikipedia, the free encyclopedia
- A set-theoretic operation typified by the jth projection map, written , that takes an element of the Cartesian product to the value .
- A function that sends an element x to its equivalence class under a specified equivalence relation E, or, equivalently, a surjection from a set to another set. The function from elements to equivalence classes is a surjection, and every surjection corresponds to an equivalence relation under which two elements are equivalent when they have the same image. The result of the mapping is written as [x] when E is understood, or written as [x]E when it is necessary to make E explicit.
- Halmos, P. R. (1960), Naive Set Theory, Undergraduate Texts in Mathematics, Springer, p. 32, ISBN 9780387900926.
- Brown, Arlen; Pearcy, Carl M. (1995), An Introduction to Analysis, Graduate Texts in Mathematics, 154, Springer, p. 8, ISBN 9780387943695.
- Jech, Thomas (2003), Set Theory: The Third Millennium Edition, Springer Monographs in Mathematics, Springer, p. 34, ISBN 9783540440857.
|This set theory-related article is a stub. You can help Wikipedia by expanding it.|