Transforms Aronszajn to Sikorski subcartesian spaces.
problem Mapping between subcategories of differential spaces.
method Constructs a natural transformation.
result Establishes a relationship between Aronszajn and Sikorski subcartesian spaces.
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5 results for “Sikorski”
Smooth maps on convex setsmath.DG
The paper explores different smooth map notions on convex sets and their relationships.
problem Exploring and comparing different smooth map notions on convex sets.
method Constructing a function that doesn't extend to a smooth function on any open neighborhood but does for functions.
result Diffeological and Sikorski smoothness notions do not coincide for all convex sets.
Constructs differential forms on -ringed spaces.
problem Developing a theory of differential forms for non-manifold spaces.
method Functorial construction of differential forms on local -ringed spaces.
result Stokes' theorem holds for integrated forms on simplices.
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only proper, the reduced nonlinear control system need not be smooth. Using the smooth …
Comparative Smootheologymath.DG
We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Frölicher, Sikorski, Smith, and Souriau. The method of comparison is to construct functors between the categories that enable us to see how the categories relate to each other. This produces a diagram…