C-spaces and simplicial complexes

Abstract

Given a class Open image in new window of simplicial complexes G, we introduce the notion of a Open image in new window -C-space. In the definition of a C-space, open disjoint families vi refine coverings ui. The nerves of these families are zero-dimensional complexes. In our definition, the nerve of a family vi must embed in the complex Gi of the class Open image in new window . We give a complete characterization of bicompact Open image in new window -C-spaces.