On model structure for coreflective subcategories of a model category

Let C be a coreflective subcategory of a cofibrantly generated model category D. In this paper we show that under suitable conditions C admits a cofibrantly generated model structure which is left Quillen adjunct to the model structure on D. As an application, we prove that well-known convenient categories of topological spaces, such as k-spaces, compactly generated spaces, and $Δ$-generated spaces {DN} (called numerically generated in {KKH}) admit a finitely generated model structure which is Quillen equivalent to the standard model structure on the category Top of topological spaces.