The function $f: (0,1) \to \mathbb R $ defined by $f(x) := 1/x$ is not uniformly continuous, but it is continuous.
88259
prove that $\frac{1}{x}$ is not uniformly continuous on $(0,1)$
97619
Which function ($f$) is continuous nowhere but $|f(x)|$ is continuous everywhere?
135449
Prove: $\frac1x$ is not a uniformly continuous function
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 $\mathbb{R}$
1986
Show $1/(1+ x^2)$ is uniformly continuous on $\Bbb R$.
131992
A problem on continuous functions
12349
a construction of a continuous function from a normal space to [0,1]
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
30036
Function in $H^1$, but not continuous
24306
Is there a continuous function $f(x)$ such that the inverse function is $1/f(x)$?
85092
Proving $ f(x) = x^2 $ is not uniformly continuous on the real line
59519
What about the continuity of these functions in the uniform topology?
114813
Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact.
55368
$f$ is continuous, if $f_n$ continuous and $f_n\to f$ uniformly
62723
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$