Zeros of discontinuous functional is dense.
62999
Linear functional on a Banach space is discontinuous then its nullspace is dense.
95294
Dense subset of $C[0,1]$ which preserves rationals
158011
$C_c^{\infty}(\mathbb R^n)$ is dense in $W^{k,p}(\mathbb R^n)$
14896
Prove: the set of zeros of a continuous function is closed.
28191
How to show that a set of discontinuous points of an increasing function is at most countable
4381
Proof that the set of irrational numbers is dense in reals
131000
A proof of a criterion of vanishing of a function.
150833
Discontinuities of the derivative of a differentiable function on closed interval
140445
Sequence of continuous functions whose pointwise limit is discontinuous
137883
Cardinality of the set of all (real) discontinuous functions
65876
A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
43254
If $A\subseteq\mathbb N$ and $\sum\limits_{a\in A}\frac1a$ converges then $A$ has natural density $0$
38886
Discontinuous function on Q
144362
The construction of a Vitali set
127678
A partition of the unit interval into uncountably many dense uncountable subsets
22865
Sine function dense in $[-1,1]$