$f(x + y) = f(x) + f(y)$. Show that $f$ is continuous.
74950
Show a function for which $f(x + y) = f(x) + f(y) $ is continuous at zero if and only if it is continuous on $\mathbb R$
72694
Proving that $f(x) = g(x)$ for some $x \in [a,b]$ if $f,g$ continuous, $f(a)  g(b)$
113975
Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function
130299
Prove that if a function $f: X\to Y$ continuous then its graph is closed
90565
If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
136011
Must $f$ be continuous?
131992
A problem on continuous functions
118207
Prove that the product of two continuous functions is continuous
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$
74364
Show that function $f$ has a continuous extension to $[a,b]$ iff $f$ is uniformly continuous on $(a,b)$
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
139744
For a continuous function $f$ show $\exists c\in (0,1)$ s.t $f(c)=3c^2$
144614
If $f$ is continuous on $[a,b]$ and $F(x) = \sup f([a,x])$. Prove that $F$ is continuous on $[a,b]$ .
117502
Proving that a certain continuous function is surjective.
143174
property of continuous function