New posts in Uniform Continuity

If $f(x+1/n)$ converges to a continuous function $f(x)$ uniformly on $\mathbb{R}$, is $f(x)$ necessarily uniformly continuous?

If $f$ is uniformly continuous on two open sets with a non-empty intersection, then $f$ is uniformly continuous on their union

Uniformly Continuous on $C^1[a,b]$

Why is it enough for $\lim\limits_{h \to 0} \vert f(x+h)-f(x)\vert = 0$ to show uniform continuity

How come the $\epsilon-\delta$ definition of continuity is preferred over the sequential definition of continuity?

What is the intuition behind uniform continuity?

Give an example of a function that is bounded and continuous on the interval [0, 1) but not uniformly continuous on this interval.

Is $f(x)=\frac{1}{x+1} \cos x^2$ uniformly continuous?

uniformly continuous function $f$ such that $\sum 1/f(n)$ is convergent?

Bounded Harmonic Functions on the Disk