Positive continuous $f_n:\mathbb{R}\to\mathbb{R}$ such that $\{f_n(x)\}$ is unbounded $\iff$ $x\in\mathbb{Q}$.
99117
Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
74501
$\delta : C([0,1])\to\mathbb{R}$, $f\mapsto f(0)$, with sup-norm is bounded but unbounded with one-norm.
88586
show that every continuous real-valued function defined on $S_{\mathbb{\Omega}}$ is eventually constant
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
136594
Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
27800
For continuous function $ f:\mathbb S^1 \to \mathbb R$ there exists uncountably many distinct points $x,y$ such that $f(x)=f(y)$
111635
Show that if $f(z)$ is a continuous function on a domain $D$ such that $f(z)^N$ is analytic for some integer $N$, then $f(z)$ is analytic on $D$.
44144
If $f:[a,b]\to \mathbb R$ is continuous then so is $\max_{t\in [a,x]}f(t)$?
110458
Show that if $f$ is continuous on $(0,1)$ and $\lim_{x \to 0}f(x) = + \infty$ then $f$ is not uniformly continuous
131060
Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
98772
Continuity of a function in $\mathbb{R}$
136011
Must $f$ be continuous?
43189
Examples of continuous functions $f : \mathbb{R} \to \mathbb{R}$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
111076
If $f$ is non-constant and entire, prove that there exists a $z_0 \in C$ such that $f(z_0)$ is a positive real number