8.1. Pointwise Convergence
Example 8.1.8 (a): Pointwise Convergence does not preserve Continuity
Find a pointwise convergent sequence of functions, each of which is
continuous, but whose limit function is not continuous.
Let f_{n}(x) = x^{n} for 0 [0, 1] and define Then:
Thus, pointwise convergence does not preserve continuity. 
