# Math Help - epislon chain problem

1. ## epislon chain problem

Please help with this problem, Im stuck.

metric space (M,d)

Prove:

Given p $\in$ M, the set of points q such that there exists a $\epsilon$-chain joining p and q is both open and closed in M. Conclude that in a connected metric space, any two points can be $\epsilon$-chained to each other.

2. Originally Posted by ElieWiesel
metric space (M,d)
Prove:
Given p $\in$ M, the set of points q such that there exists a $\epsilon$-chain joining p and q is both open and closed in M. Conclude that in a connected metric space, any two points can be $\epsilon$-chained to each other.
I think that you need to define $\epsilon-\text{chained}$.