Prove or disprove If f is continuous and g is dicontinuous then f + g is discontinuous
124444
If $f$ s discontinuous at $x_0$ but $g$ is continuous there, then $f+g$?
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
149095
$f(\mathbb{R}\setminus \mathbb{Q}) \subseteq \mathbb{Q}$ and $f(\mathbb{Q}) \subseteq \mathbb{R}\setminus \mathbb{Q}$ imply that $f$ is not continuous
66391
Show that $f(x+y)=f(x)+f(y)$ implies $f$ continuous $\Leftrightarrow$ $f$ measurable
53497
Prove that the function is continuous and differentiable (not as easy as it sounds imo)
140445
Sequence of continuous functions whose pointwise limit is discontinuous
47381
If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
7876
If $f(x+y)=f(x)+f(y) ,\forall\;x,y\in\Bbb{R}$, then if $f$ is continuous at $0$, then it is continuous on $\Bbb{R}.$
105652
Suppose $f: \mathbb{R} \to \mathbb{R}$ is function such that $f^3$ is continuous on $\mathbb{R}$. Prove that $f$ is continuous on $\mathbb{R}$
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
110112
Proving a function is Lipschitz continuous
104044
Prove continuous functions $f$ and $g$ are equal
16291
Discontinuous derivative.
62817
Functions which are Continuous, but not Bicontinuous
3518
Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
83204
Is every $G_\delta$ set the set of continuity points of some function $f$?