Simplicial complexes triangulating infinite-dimensional manifolds
Let K be a (not necessarily locally finite) countable simplicial complex, and let \(| K|_ w\), \(| K|_ m\) denote, respectively, the union of the simplices of K with the weak, metric topologies. The main result of this paper shows that if each simplex of K is a Z-set in \(| K|_ m\) then K is a combinatorial \(\infty\)-manifold. It then follows that these two conditions are equivalent to each other and a number of other conditions including the author's previously conjectured equivalent conditions that \(| K|_ w\) is an \({\mathbb{R}}^{\infty}\)-manifold and that \(| K|_ m\) is a \(\sigma\)- manifold.
scientific article; zbMATH DE number 4062164
scientific article