as in $\displaystyle f_n(x) = c$ for all $\displaystyle n$ and $\displaystyle x$ converging uniformly to $\displaystyle f(x) = c$ (where $\displaystyle c$ is a constant)?
you tell me, does this satisfy the definition of what it means to be uniformly convergent?
I would say yes it is uniformly convergent. I have a line x=2.
So f_n(x)=2 and f(x)=2. Their difference is 0 implying uniform convergence.
x = 2 is a vertical line. so unless you are interpreting it like $\displaystyle f_n (y) = 2$ or something, it won't make sense. but yeah, a difference of zero everywhere implies uniform convergence