Is the limit function $f$ continuous if $f_n(x_n)\to f(x)$?
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
71001
Do continuous linear functions between Banach spaces extend?
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
28413
Limit of a continuous function
127538
Show $f(x)=x\ln x$ is not uniformly continuous
143695
Is an increasing, bounded and continuous function on $[a,+\infty)$ uniformly continuous?
34940
Continuity of $f(x) = x^n$
140445
Sequence of continuous functions whose pointwise limit is discontinuous
29180
If $f(x/n)\to0$ when $n\to\infty$, for every $x$ and $f$ is continuous, then $f(x)\to0$ when $x\to0$, or not?
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
42817
proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
53738
Monotone functions and continuity
22989
A doubt on the definition of limit of a function definition
51156
Function is Continuous When Restricted to Closed Sets Which Cover the Space
72847
Does $f(x)$ is continuous and $f = 0$ a.e. imply $f=0$ everywhere?
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?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$