# Homework Help: Fibers of a map

1. Oct 26, 2008

### SNOOTCHIEBOOCHEE

1. The problem statement, all variables and given/known data

Prove that the nonempty fibers of a map form a partition of the domain.

3. The attempt at a solution

Ok so we have some map phi: S -->T

And we want to show that its pre-image phi-1(t) = {s in S | phi(s)=t} forms a partition of the domain.

Im really confused here. I assume that it is talking about that domian of phi which is S (i think) but i have no clue how this preimage forms partitions.

Last edited: Oct 26, 2008
2. Oct 26, 2008

### SNOOTCHIEBOOCHEE

any thoughts?

3. Oct 26, 2008

### Dick

Doesn't phi^(-1)(t) for t in T constitute a set of non-overlapping sets that cover S? Look up partition.

4. Oct 26, 2008

### SNOOTCHIEBOOCHEE

Well a partition P of S is a subdivision of S into nonoverlapping subsets

How do you know phi^(-1)(t) for t in T constitute a set of non-overlapping sets that cover S

5. Oct 27, 2008

### morphism

Prove it. Can any two fibers that correspond to different elements of T intersect nontrivially? Is there anything in S that doesn't lie in a fiber?