Example 2

Let X, $X',X''$ be B-spaces and let $p,p',p''$ be their respective projections. The product B-space $(X\times_BX')\times_BX''$ is the topological subspace $X\times_BX'\times_BX''$ of $X\times X'\times X''$ formed by the triples $(x, x', x'')$ such that $p(x) =p'(x') =p''(x'')$, endowed with the projection $q: X\times_BX'\times_BX''\rightarrow B$ defined by $q(x, x', x'') =p(x)$.