Checking for continuity of functions of $\mathbb{R}^2$
104227
How to obtain the limit of $xy\log(x^2+y^2)$ when $(x,y)\to(0,0)$ without using polar coordinates or L'Hôpital?
157603
Continuity $\iff$ Preimage is closed whenever set is closed
141423
The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
125682
Proof verification: the product of two continuous functions is continuous
67289
Continuity of the Characteristic Function of a RV
87239
Prove functions defined by sup and inf are continuous
136011
Must $f$ be continuous?
40209
$f : S^1 \to\mathbb R$ is continuous then $f(x)=f(-x)$ for some $x\in S^1$
64619
Continuity of a function of product spaces
153730
Show that $f(x)=x^2$ is continuous at $a=2$ using the $\delta-\epsilon$ definition of continuity.
58664
Proving a function is continuous for a fixed variable
29276
technique of proving continuity complex function
83204
Is every $G_\delta$ set the set of continuity points of some function $f$?
72044
prove $x \mapsto x^2$ is continuous
46642
Continuity of $\sin(x)/x$
53627
Proving continuity of $f$
60700
Continuity of a function to the integers