Topological Product with Singleton

Theorem
Let $$T_1$$ and $$T_2$$ be topological spaces.

Let $$a \in T_1, b \in T_2$$.

Let $$T_1 \times T_2$$ be the topological product of $$T_1$$ and $$T_2$$.

Then:
 * $$T_1$$ is homeomorphic to the subspace $$T_1 \times \left\{{b}\right\}$$ of $$T_1 \times T_2$$;
 * $$T_2$$ is homeomorphic to the subspace$$\left\{{a}\right\} \times T_2$$ of $$T_1 \times T_2$$.