Let $f$ be a function continuous on the right at every point of $\mathbb R$. Show that the set of points of continuity of $f$ is dense in $\mathbb R$
67866
If $f:\mathbb{R}\to\mathbb{R}$ is a left continuous function can the set of discontinuous points of $f$ have positive Lebesgue measure?
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
139612
Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
44574
Continuity of absolute value of a function
151410
Inequality of continuous functions
131992
A problem on continuous functions
140052
Show that $f(X - D) \cap f(D) = \varnothing$ with $f$ continuous in $X$, $D$ dense in $X$ and $f|_{D}$ homeomorphism
145919
If $f: \Bbb{R}\rightarrow\Bbb{R}$ is continuous at $0$ and $f(x)=f(2x)$ for each $x\in\Bbb{R}$ then $f$ is constant.
3772
About the continuity of the function $f(x) = \sum\limits_k2^{-k}\mathbf 1_{q_k \leq x}$
73594
Existence of continuous function $f$ on $\Bbb R$ which vanishes exactly on $A\subset \Bbb R$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
12003
Cardinality of set of real continuous functions
9406
Compactness of $(M, d)$ in terms of continuous functions $f:M\to \mathbb R$