Kernel_(set_theory)
Kernel (set theory)
Equivalence relation expressing that two elements have the same image under a function
In set theory, the kernel of a function (or equivalence kernel[1]) may be taken to be either
- the equivalence relation on the function's domain that roughly expresses the idea of "equivalent as far as the function can tell",[2] or
- the corresponding partition of the domain.
This article needs additional citations for verification. (December 2009) |
An unrelated notion is that of the kernel of a non-empty family of sets which by definition is the intersection of all its elements:
This definition is used in the theory of filters to classify them as being free or principal.