Is there a uniformly continuous function $f:\mathbb R \to \mathbb R$ such that $a_{n+1}=f(a_n)$?
113740
Find a uniformly continuous function such that $a_{n+1}=f(a_n)$
110885
Does there exists a continuous surjection from $\mathbb{R}$ to $\mathbb{R}^2$?
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
55749
Compactly supported continuous function is uniformly continuous
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
52922
let $f \colon [a,b] \to \mathbb{R}$ be continuous on $[a,b]$ and..
99117
Existence of a sequence of positive continuous functions on $\mathbb R$ which is unbounded precisely on $\mathbb Q$
138105
Let $f$ and $g$ be continuous at $ x=a$, with $f(a)<g(a)$. Prove that there exists a neighborhood $I$ of a such that $f(x)<g(x)$ for all $x \in I$.
24017
Let $f: \Bbb R \to [0,\infty)$ be a continuous function such that $g(x)=(f(x))^2$ is uniformly continuous. Which of the following is always true?
142645
$f_n$ converges uniformly on $[a,b]$ to some function $f$
59519
What about the continuity of these functions in the uniform topology?
108057
If $(f_n)\to f$ uniformly and $f_n$ is uniformly continuous for all $n$ then $f$ is uniformly continuous
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
128911
Continuous extension of a real function
51247
$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?