Can $f$ be extended to a continuous function from $S$ to $\Bbb R$?

Question

If $S = \{(x,y) \in \Bbb R^2 \mid -1 \leq x \leq 1 \text{ and } {-1} \leq y \leq 1\}$

and $T = S - (0,0)$ and $f$ be a continuous function from $T$ to $\Bbb R$,

then how can I disprove or prove that $f$ can be extended to a continuous function from $S$ to $\Bbb R$?

Can anyone please help me out?

Answer 1

Hint: take $f(x,y)=\frac{1}{x^2+y^2}$.