If $f$ is compact is $f$ continuous?
136011
Must $f$ be continuous?
44574
Continuity of absolute value of a function
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
55749
Compactly supported continuous function is uniformly continuous
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
4171
If $f$ is locally Lipschitz on $X$ and $X$ is compact, then $f$ is Lipschitz on $X$.
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
32571
Is the maximum function of a continuous function continuous?
2118
Are continuous functions with compact support bounded?
150554
proof that $f'$ is continuous at $a$
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
121957
Is $p\mapsto \|f\|_p$ continuous?
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
127868
If $f$ is nonnegative and integrable then $F(x) = \int_{-\infty}^x f$ is continuous.
157821
Let $S$ be a finite set. Show that any function $f: S \rightarrow \mathbb{R}^n$ is continuous on S. What if $S$ is countably infinite?
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point