Does Converges Uniformly Imply Continuous?
If a Sequence of Functions Fn(X) Defined on D Converges Uniformly to a Function F(X), and If Each Fn(X) Is Continuous on D, Then the Limit Function F(X) Is...
If a sequence of functions fn(x) defined on D converges uniformly to a function f(x), and if each fn(x) is continuous on D, then the limit function f(x) is also continuous on D.
Does uniform convergence imply continuous?
Theorem. (Uniform convergence preserves continuity.) If a sequence fn of continuous functions converges uniformly to a function f, then f is necessarily continuous.
Are convergent series continuous?
Hence it follows that the sum of any series of continuous functions, convergent in some interval, is continuous on a dense set of points of the interval.
Alexander Ross has covered the video game industry for a decade, writing deep dives on game design, esports tournaments, VR developments, and gaming culture.
