I am looking for the technical term for an element of a transformation semigroup that sends everything to one state. The best term I could think up was filter.
For those that don't know a trasformation is like a permutation, except you can have repeated entries.
Identity permutation/transformation
[1,2,3,4] [1->1, 2->2, 3->3, 4 ->4]
Legal permutation/transformation
[2,1,4,3] [1->2, 2->1, 3->4, 4->3]
Illegal permutation, legal transformation:
[1,1,3,4] [1->1, 2->1, 3->3, 4->4]
Transformations I would like to know the technical term for:
[1,1,1,1]
[2,2,2,2]
[3,3,3,3]
[4,4,4,4]
