 Weak topology of a simplicial realization

Give the geometric realization of an abstract simplicial complex the quotient topology obtained by gluing the disjoint union of its standard simplexes along their labelled faces. A subset $U$ is open exactly when $U\cap |\sigma |$ is open in every closed geometric simplex $|\sigma |$. This is the weak realization topology. It is the topology of its CW complex structure; the word weak here refers to the simplexwise test, rather than to the weak topology of a topological vector space. A map out of the realization is continuous exactly when its restriction to every simplex is continuous.