There are 2 ways of saying a function, , is uniformly continuous
A. For every , there exists a such that
whenever and
B. For every , there exists a such that
whenever and
Prove f satisfies A if and only if it satisfies B
This is a confusing proposition. I think if f satisfies B, then it obviously satisfies A, but I could be mistaken.
And if it satisfies A, how do I go about demonstrating B?
Thanks in advance for the help
As a curiosity:
We say that is obtained by relaxing the strict inequalyty .
Fernando Revilla