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Topologies on product and coproduct Frölicher spaces

Batubenge T. A., Tshilombo M. H.

Demonstratio Mathematica

2014

Vol. 47, nr 4

1012--1024

In this paper, the topologies underlying a product Frölicher space and a coproduct Frölicher space are defined and compared. It is shown that the product topology, which is equal to the one induced by structure functions, is the weakest one in which all projections are continuous. On the other hand, it is proved that the three topologies arising from the coproduct structure are equal.

Topologies and smooth maps on initial and final objects in the category of Frolicher spaces

Batubenge A., Tshilombo H.

Demonstratio Mathematica

2009

Vol. 42, nr 3

641-655

In this paper, we show that when the Frolicher smooth structure is induced on a subset or a quotient set, there are three natural topologies underlying the resulting object. We study these topologies and compare them in each case. It is known that the topology generated by strucure functions is the weakest one in which all functions and curves on the space are continuous. We show that on a subspace, it is rather the trace topology which has this property, while the three topologies are coincident on the quotient space. We construct a base for the Frolicher topology and using either a base or a subbase in the sense of A. Frolicher [9], we characterise the morphisms of this category.

An approach to Hamiltonian mechanics on glued symplectic pseudomanifolds

Batubenge A., Sasin W.

Demonstratio Mathematica

2008

Vol. 41, nr 4

941-960

We define a class of Frolicher spaces locally diffeomorphic to Frolicher subspaces of the Euclidean space Rn and we call them pseudomanifolds. These differential constructs carry symplectic geometry so that Hamiltonian systems are naturally introduced. When gluing together symplectic pseudomanifolds which intersect transversally, it turns out that up to an equivalence relation, the glued space is symplectic and smooth integral curves extend to singular points.

Sikorski and Frolicher CW-complexes compared

Ntumba P. P.

Demonstratio Mathematica

2005

Vol. 38, nr 1

207--221

In this paper we analyze the underlying topological space of a Sikorski CW-complex and the close relationship between Sikorski CW-complexes and Frolicher CW-complexes. Sikorski and Frolicher CW-complexes are analogues of CW-complexes in the categories of differential spaces (a la Sikorski) and Frolicher spaces relatively.