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1
Content available remote Aronszajn and Sikorski subcartesian differential spaces
Cushman Richard, Śniatycki Jędrzej
Bulletin of the Polish Academy of Sciences. Mathematics
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2021
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Vol. 69, no. 2
171--180
EN
We construct a natural transformation between the category of Aronszajn subcartesian spaces and the category of subcartesian differential spaces, which is a subcategory of Sikorski differential spaces.
2
Content available remote Slice theorem for differential spaces and reduction by stages
Lusala T., Śniatycki J.
Demonstratio Mathematica
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2014
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Vol. 47, nr 1
192--210
EN
We show that the space P/G of orbits of a proper action of a Lie group G on a locally compact differential space P is a locally compact differential space with quotient topology. Applying this result to reduction of symmetries of Hamiltonian systems, we prove the reduction by stages theorem.
3
Content available remote Integration on differential spaces
Dziewa-Dawidczyk D., Pasternak-Winiarski Z.
Demonstratio Mathematica
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2014
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Vol. 47, nr 3
748--762
EN
The generalization of the n-dimensional cube, an n-dimensional chain, the exterior derivative and the integral of a differential n-form on it are introduced and investigated. The analogue of Stokes theorem for the differential space is given.
4
Content available remote On linear operators consistent with a subspace in differential spaces
Multarzyński P.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
233-244
EN
Linear operators on function and abstract algebras are considered and their consistency with an arbitrary subset or an ideal is studied. Then the consistency concept is formulated for general Poisson brackets in commutative algebras.
5
Content available remote Weil homomorphism in non-commutative differential spaces
Jagodziński T., Sasin W.
Demonstratio Mathematica
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2005
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Vol. 38, nr 2
507--516
EN
In this paper we construct Weil homomorphism in locally free module over a non-commutative differential space, which is a generalization of Sikorski differential space [6]. We consider real case, but the complex case can be done analogusly.
6
Content available remote K-differential spaces as sheaves. Induced and coinduced structure
Piątkowski A.
Demonstratio Mathematica
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2005
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Vol. 38, nr 2
495--506
EN
Any K-differential space determines the sheaf of germs of its elements. We consider the K-differential space induced and coinduced by a single mapping. In this special case, we compare the sheaf of germs of the induced K-differential space with the inverse image of the sheaf of germs of a given K-differential space, and the sheaf of germs of the coinduced K-differential space with the image of the sheaf of germs of a given K-differential space.
7
Content available remote On the leaves of a prefoliation of a K-differential space
Piątkowski A.
Demonstratio Mathematica
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2004
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Vol. 37, nr 3
689--696
EN
The definition of a prefoliation (M,F) of a K-differential space and the theorem about regularity of the inclusion of a leaf of a prefoliation are reminded. An example of a pair (M, F) of SC-differential spaces with the same set of points, which shows that even if the identity of .M is an immersion F -> M and (top M, top F) is a topological foliation in the sense of Ehresmann then (M, F) has not to be a prefoliation, is given. In the end, we show that if L is a proper leaf of a prefoliation (M, F) then the both structures of a K-differential spaces coincide on L.
8
Content available remote On some right invertible operators in differential spaces
Multarzyński P.
Demonstratio Mathematica
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2004
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Vol. 37, nr 4
905--920
EN
In this paper we consider the right invertibility problem of some linear operators defined on the algebra of smooth function on a differential space.
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