Cauchy Continuous function is continuous??
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
7876
If $f(x+y)=f(x)+f(y) ,\forall\;x,y\in\Bbb{R}$, then if $f$ is continuous at $0$, then it is continuous on $\Bbb{R}.$
94109
$f$ a real, continuous function, is it measurable?
98772
Continuity of a function in $\mathbb{R}$
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
86327
If the absolute value of a function is continuous, is the function continuous?
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
53812
Metric is continuous function
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
66691
Real function continuous on closed interval implies it is bounded - over-simple proof??
150770
Why is $f^n(\xi(x))$ continuous over $x$?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
34344
Is a function that maps every compact set to a compact set continuous?
134575
Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
128911
Continuous extension of a real function
30590
Are "most" continuous functions also differentiable?
85890
When is the Laplace transform of a function continuous?