Final answer:
The assertion that a sequence of functions which is uniformly convergent on two separate intervals must be convergent on the union of those intervals is false, because uniform convergence on each part does not guarantee uniform convergence on the combined interval.
Step-by-step explanation:
The question is whether a sequence of functions that is uniformly convergent on two separate intervals implies it is convergent on the union of those intervals. The assertion is false. Uniform convergence on separate intervals does not necessarily imply uniform convergence on their union. This is because uniform convergence requires that all points in the interval converge to the function within the same bound. If the intervals are disjoint, there can be issues at the boundary points when combining intervals. For instance, the sequence could converge uniformly on each interval, but with different limits, causing a discontinuity at the point where the intervals meet.