WebDec 18, 2015 · Abstract This survey paper highlights a series of results in recent research on topology, geometry and categorical properties of spaces provided with a new structure in the mathematical... WebDifferential Geometry of Microlinear Frolicher Spaces IV-1. E → M at x ∈ E is cal led a Dn+1 -tangential over the bund le π : E → M at x if it acquiesces in the fol lowing two conditions: 1. bπn+1,n (∇x ) is a Dn -tangential over the bund le π : E → M at x. 2. Differential Geometry of Microlinear Frolicher Spaces IV-2
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Webof a Frolicher space X and a Weil algebra W, another Frolicher space X ® W, called the Weil prolongation of X with respect to W, which naturally extends to a bifunctor FS x W ---+ FS, where FS is the category of Frolicher spaces and smooth mappings, and W is the category of Weil algebras. We have shown in [15] that Theorem 1. WebDiffeological spaces are a Cartesian-closed, complete, and cocomplete category containing all infinite dimensional manifolds, and in fact even form a quasi-topos. Diffeological spaces, concisely, are nothing more than concrete sheaves on the site of Cartesian manifolds (manifolds of the form R n ): http://ncatlab.org/nlab/show/concrete+sheaf the pointe at conway apartments
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WebJan 1, 2004 · This survey paper highlights a series of results in recent research on topology, geometry and categorical properties of spaces provided with a new structure in the … WebWe investigate some algebraic properties on these spaces whose subsequent geometric properties are mostly similar to those of smooth manifolds, except for the invariance of … WebJan 10, 2016 · In this work we introduce a class of Sikorski differential spaces (M;D) called pre-Frolicher spaces, on which the process of yielding a Frolicher structure on the underlying set M is D preserving, their category we denote by preFrl. We investigate some algebraic properties on these spaces whose subsequent geometric properties are … sidewinder electric guitar