Projection Map

Definition

Consider a Product Topology ${\prod }_{i\in I}{X}_i$. The $j$-th projection map return $j$-th value of the topology. ${\mathrm{proj}}_j={\pi }_j:{\prod }_{i\in I}{X}_i\to X_j,{\pi }_j(x_1,x_2,\dots ,x_j,\dots )=x_j$

Facts

A projection map is a Quotient Map.

A projection map is a Continuous Function