Given a close 3-form H ∈ Ω 0 (M), we define a twisted bracket on the space Γ(TM) ⊕ Ω 0 (M). We define the group of H-twisted Hamiltonian symmetries Ham(M, J;H) as well as Hamiltonian action of Lie group and moment map in the category of (twisted) generalized complex manifold, which leads to generalized complex reduction much the same way as symplectic reduction is constructed. The definitions a...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

There is a natural topology on the symmetric group on an infinite set Ω . If Ω is countable , the topology is derived from a metric , and the group is complete . This paper gives an account of this topology , including translations of topological concepts for permutation groups , the use of Baire category and Haar measure , and some results about confinitary permutation groups which are motivat...

We prove the existence of smooth closed hypersurfaces of prescribed mean curvature homeomorphic to S for small n, n ≤ 6, provided there are barriers. 0. Introduction In a complete (n+1)-dimensional manifold N we want to find closed hypersurfaces M of prescribed mean curvature. To be more precise, let Ω be a connected open subset of N , f ∈ C(Ω̄), then we look for a closed hypersurface M ⊂ Ω such...

Suppose that Ω is a subdomain of Rn and G is a non-elementary K-quasiconformal group. Then G is a Lie group acting on Ω. Hilbert-Smith Conjecture states that every locally compact topological group acting effectively on a connected manifold must be a Lie group. Recently Martin [8] has solved the solution of the Hilbert-Smith Conjecture in the quasiconformal category (Theorem 1.2): Theorem 1. Le...

Results of Sierpiński and others have shown that certain finite-dimensional product sets can be written as unions of subsets, each of which is “narrow” in a corresponding direction; that is, each line in that direction intersects the subset in a small set. For example, if the set ω × ω is partitioned into two pieces along the diagonal, then one piece meets every horizontal line in a finite set,...

let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .