Simplicial Complexes and Open Subsets of Non-Separable LF-Spaces

Abstract

Abstract Let F be a non-separable LF-space homeomorphic to the direct sum , where . It is proved that every open subset U of F is homeomorphic to the product |K| × F for some locally finite-dimensional simplicial complex K such that every vertex v ∈ K(0) has the star St(v, K) with card St(v, K)(0) < 𝒯 = sup 𝒯n (and card K(0) ≤ 𝒯 ), and, conversely, if K is such a simplicial complex, then the product |K| × F can be embedded in F as an open set, where |K| is the polyhedron of K with the metric topology.