Continuous_Mapping_to_Topological_Product

Let $T = T_1 \times T_2$ be a product space of two topological spaces $T_1$ and $T_2$. Let $\pr_1: T \to T_1$ and $\pr_2: T \to T_2$ be the first and second projections from $T$ onto its factors. Let $T'$ be a topological space. Let $f: T' \to T$ be a mapping. Then $f$ is continuous $\pr_1 \circ f$ and $\pr_2 \circ f$ are continuous.