Savitch's theorem and time relation We know that $NTIME(t(n)) \subseteq DSPACE(t(n))$ and we know - by Savitch's theorem - that $NSPACE(s(n)) \subseteq DSPACE(s^2(n))$.

By the space/time relation $(s(n) \leq t(n))$ I know that $NTIME(t(n)) \subseteq NSPACE(t(n))$, then by Savitch's theorem $NSPACE(t(n)) \subseteq DSPACE(t^2(n))$ and not $DSPACE(t(n))$, as stated above.

Where am I wrong?
I believe you left out big-Os around those bounds.

In any case, $\; \{0\} \subseteq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1\hspace{-0.03 in}\} \;$ and $\; \{0\} \subseteq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1,\hspace{-0.04 in}2\hspace{-0.02 in}\}$ , $\;$ even though $\: \{\hspace{-0.02 in}0,\hspace{-0.05 in}1\hspace{-0.03 in}\} \neq \{\hspace{-0.02 in}0,\hspace{-0.05 in}1,\hspace{-0.04 in}2\hspace{-0.02 in}\}$ .