Show continuous $f_1 : ~ ]a, b[ \to \mathbb{R}$ is uniform continuous $\Leftrightarrow$ continuous $f_2:~ [a, b] \to \mathbb{R}$ exists with...
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
53627
Proving continuity of $f$
29154
$f$ is continuous and open implies $f$ injective
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
126461
Show that $g:I\to\mathbb{R}$ is continuous and $f:(x-x_0)g(x)$ is differentiable
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
132946
Continuous and bounded imply uniform continuity?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
16735
If $f,g:X \to Y$ are continuous and $Y$ is $T_2$, then $\{x \in X\,|\,f(x)=g(x)\}$ is closed
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$
86472
$f:\mathbb R \to \mathbb R^n$ be such that $G(f):=\{(x,f(x)):x \in \mathbb R\}$ is closed and connected in $\mathbb R^{n+1}$ , is $f$ continuous ?
51247
$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
124779
Intuition for uniform continuity of a function on $\mathbb{R}$
40297
Proof of uniform limit of Continuous Functions
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
36166
Uniform continuity on (0,1) implies boundedness
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous