on the no existence of a continuous extension of the identity function on $c_0$ to $l^{\infty}$ not equal to $I$
119003
Complement of $c_{0}$ in $\ell^{\infty}$
143798
Prove that, there exists no continuous function $f:\mathbb R\rightarrow\mathbb R$ with $f=\chi_{[0,1]}$ almost everywhere.
133874
Proof that $\lim_{n\to\infty}{\sin{100n}}$ does not exist
115878
Continuous unbounded but integrable functions
33114
Uniqueness of a continuous extension of a function into a Hausdorff space
143708
$L^1$ and $L^{\infty}$ are not reflexive
63453
A proof of the fact that the Fourier transform is not surjective from $\mathcal{L}^1(\mathbb{R})$ to $C_0( \mathbb{R})$
79307
How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
13732
$||f||_p\to ||f||_\infty$ under general assumptions
130916
Proving the identity functions is continuous iff $\tau_1\supseteq\tau_2$
113450
Construction of a function which is not the pointwise limit of a sequence of continuous functions
106843
Give an example where $\int_{\bar A} f$ exists but $\int_A f$ does not for a continuos $f$ on a bounded open subset $A$ of $\mathbb{R}^n $
234
No continuous function switches $\mathbb{Q}$ and the irrationals
41201
How prove there is no continuous functions $f:[0,1]\to \mathbb R$, such that $f(x)+f(x^2)=x$.
12272
Why $a$ is not an essential singularity and how $f$ can be extended
113790
$\overline{B_1(0)}$ is not weakly* sequentially compact in $(l^\infty)$'
40576
Intermediate value property problem and continuous function