Proving continuity for function $f: \mathbb{R^2} \rightarrow \mathbb{R}$ given by $f(x,y) = \frac{xy}{x^2 + y^2}$
23294
Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
87239
Prove functions defined by sup and inf are continuous
142459
Continuity of a Function in Terms of Closure and Interior
62723
If $f\colon \mathbb{R} \to \mathbb{R}$ is such that $f (x + y) = f (x) f (y)$ and continuous at $0$, then continuous everywhere
19916
$f(x)=f(x^2+ 1/4)$ , $f$ is continuous from $\mathbb{R}$ to $\mathbb{R}$
46834
show that a distance function is continuous
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
130023
Prove that the sum of two continuous functions is continuous
118332
proof $f(\overline{A})\subseteq \overline{f(A)} \Leftrightarrow f$ continuous
77943
If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
113503
Show that exists a not decreasing function that $f:(a,b)\rightarrow \mathbb{R}$ that is continuous only in $(a,b)\setminus D$.
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
75479
Proving that this function is continuous on $G\times G$
37966
If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$
69869
if $f$ is continuous on $\mathbb{R}$ and $f(r)=0,r \in \mathbb{Q}$, then $f(x)=0,x \in \mathbb{R}$
53627
Proving continuity of $f$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$