Mixing model structures

We prove that if a category has two Quillen closed model structures (W1,F1,C1) and (W2,F2,C2) that satisfy the inclusions W1⊆W2 and F1⊆F2, then there exists a “mixed model structure” (Wm,Fm,Cm) for which Wm=W2 and Fm=F1. This shows that there is a model structure for topological spaces (and other topological categories) for which Wm is the class of weak equivalences and Fm is the class of Hurewicz fibrations. The cofibrant spaces in this model structure are the spaces that have CW homotopy type.