Is pointwise convergence continuous?
Is pointwise convergence continuous? Thus, pointwise convergence does not, in general, preserve boundedness. f(x) = { 0 if 0 ≤ x < 1, 1 if x = 1. Although each fn is continuous on [0, 1], their pointwise limit f is not (it is discon- tinuous at 1). Thus, pointwise convergence does not, in general, preserve continuity. What is meant by pointwise convergence? From Wikipedia, the free encyclopedia. In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often...