= 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.
Back to article page
