If we have a function f continuous on [a,b] is it true that f is uniformly continuous on (a,b) assuming f(a) and f(b) are defined? If so why?
What about if f(a) is not defined? For example f(x) = 1/(x^2) is continuous on [0,1] (and so is uniformly continuous on [0,1]) but is funiformly continuous on (0,1) considering f(0) is not defined? If so why?