If the fact that $f_y$ and $f_x$ are continuous can implies $f$ is continuous?
63598
Is every separately continuous function on $R^2$ continuous?
28730
product of two uniformly continuous functions is uniformly continuous
15579
Show that $f$ is uniformly continuous if limit exists
122160
$f:\mathbb R \to \mathbb R$ be a continuous such that $f(f(f(x)))=x,\forall x \in \mathbb R$ , is $f(x)=x , \forall x \in \mathbb R$?
25482
If a function is continuous and differentiable everywhere is the derivative continuous?
97975
Does factor-wise continuity imply continuity?
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
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 $\mathbb{R}$
57642
Uniform Continuity implies Continuity
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
46629
Prove if $f(x) = g(x)$ for each rational number x and $f$ and $g$ are continuous, then $f = g$
155923
continuity of $f(x,y)$ in $\mathbb R^2$.
51247
$f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
121957
Is $p\mapsto \|f\|_p$ continuous?
86327
If the absolute value of a function is continuous, is the function continuous?
132946
Continuous and bounded imply uniform continuity?
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous