Exists continuous $f_n: [0,1] \to \mathbb{R}$ that converges pointwise, as $n \to \infty$, to $\chi_\mathbb{Q}$?
92734
Existence of a sequence of continuous functions convergent pointwise to the indicator function of irrational numbers
136594
Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
94066
Prove that: {$f_n$} converges unifromly to $f$ on $E$ as $n \rightarrow \infty$ if and only if $\lim_{n\rightarrow \infty} ||f_n-f||_u = 0$
144551
Exercise on infinite series: pointwise product between convergent serie and unbounded sequence
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
79496
Holomorphic functions which converge pointwise but not almost uniformly
96729
Changing the values of an integrable function $f:[a,b] \to \mathbb R$ countably infinitely many points not a dense subset of $[a,b]$
19072
$\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
76593
Show that $f_n(z)=z^n$ converges locally uniformly on $|z|<1$ but not uniformly(?)
152280
An absolute convergence criterion in $\Bbb C$
30455
Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
55605
If $f_n(x_n) \to f(x)$ whenever $x_n \to x$, show that $f$ is continuous
153063
Uniform convergence of $f_n(x)=nx^n(1-x)$ for $x \in [0,1]$?
56567
Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
111990
Continuous function from $(0, 1]$ onto $(0, 1)$?
142645
$f_n$ converges uniformly on $[a,b]$ to some function $f$
13732
$||f||_p\to ||f||_\infty$ under general assumptions