C∞-manifolds with skeletal diffeology

We formulate and study the notion of d-skeletal diffeology, which generalizes that of wire diffeology, introducing the dual notion of d-coskeletal diffeology. We first show that paracompact finite-dimensional C∞-manifolds Md with d-skeletal diffeology inherit good topologies and smooth paracompactness from M. We then study the pathology of Md. Above all, we prove the following: For d更多