Solution
= Solution
The map
$$
g:T\to T,
\qquad g(u,v)=(uv^{-1},v),
$$
is continuous and satisfies $g\circ f=f\circ g=\operatorname{id}_T$. Therefore
$$
\boxed{\ f^{-1}(u,v)=(uv^{-1},v),\quad\text{so }f\text{ is a homeomorphism}.\ }
$$
= Solution
The map
$$
g:T\to T,
\qquad g(u,v)=(uv^{-1},v),
$$
is continuous and satisfies $g\circ f=f\circ g=\operatorname{id}_T$. Therefore
$$
\boxed{\ f^{-1}(u,v)=(uv^{-1},v),\quad\text{so }f\text{ is a homeomorphism}.\ }
$$