Projection from Metric Space Product with Euclidean Metric is Continuous/Proof 1

Proof
The Euclidean metric is an instance of the $p$-product metric:


 * $\map {d_p} {x, y} := \paren {\paren {\map {d_1} {x_1, y_1} }^p + \paren {\map {d_2} {x_2, y_2} }^p}^{1/p}$

where $p = 2$.

The result is therefore seen to be an instance of Projection from Metric Space Product with P-Product Metric is Continuous.