Abstract
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<dimM, every immersion f:M⟶N is isolated in the diffeological space D(Md,Nd) of smooth maps and the d-dimensional smooth homotopy group of Md is uncountable.
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