prove that $f$ is continuous over $[0,1]\cap\mathbf{Q}^{c}$
57233
Proof of continuity of Thomae Function at irrationals.
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
69695
$f\geq 0$, continuous and $\int_a^b f=0$ implies $f=0$ everywhere on $[a,b]$
28289
Show that $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$ is linear and continuous
115417
Continuity of $L^1$ functions with respect to translation
72044
prove $x \mapsto x^2$ is continuous
87239
Prove functions defined by sup and inf are continuous
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
111485
Let $f(x)$ be continuous on [$0,1$] to $f(x)=0$ for each $x\in[0,1]$
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
15914
Prove that any polynomial function is continuous
84510
If $f(\mathbb{C})\subset \mathbb{C}-[0,1]$ then $f$ is constant
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
34940
Continuity of $f(x) = x^n$