A Hausdorff topological space X is van der Waerden if for every sequence (xn)n∈ω in X there is a converging subsequence (xn)n∈A where A ⊆ ω contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (xn)n∈ω in X there is an IP-converging subsequence (xn)n∈FS(B) for some infinite B ⊆ ω. We show that the continuum hypothesis implies th...

Let Ω be a symmetric cone and V the corresponding simple Euclidean Jordan algebra. In [2, 5, 6, 8] we considered the family of generalized Laguerre functions on Ω that generalize the classical Laguerre functions on R. This family forms an orthogonal basis for the subspace of L-invariant functions in L(Ω, dμν), where dμν is a certain measure on the cone and where L is the group of linear transfo...

We investigate in this paper the topological stability of pairs (ω,X), where ω is a germ of an integrable 1-form and X is a germ of a vector field tangent to the foliation determined by ω.

let $a_1$, $a_2$ be unital banach algebras and $x$ be an $a_1$-$a_2$- module. applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $a_i$ into the dual space $a^*_i$ (for$i=1,2$) and such derivations  from  the triangular banach algebraof t...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

We give a new, purely holomorphic description of the holomorphic anomaly equations of the topological string, clarifying their relation to the heat equation satisfied by the Jacobi theta series. In cases where the moduli space is a Hermitian symmetric tube domain G/K, we show that the general solution of the anomaly equations is a matrix element 〈Ψ|g|Ω〉 of the Schrödinger-Weil representation of...

Donaldson’s work on Lefschetz pencils has shown that, after a slight perturbation of the symplectic form and a finite number of blow-ups, any closed symplectic manifold (M,ω) can be expressed as a singular fibration with generic fiber a smooth codimension 2 symplectic submanifold. Thus fibrations play a fundamental role in symplectic geometry. It is then natural to study smooth (nonsingular) ru...

Let G be a topological group acting continuously on an infinite compact space X. Suppose the dynamical system (X, G) is minimal, i.e., suppose that every point in X has a dense G-orbit. We show that X is coabsolute with a Cantor space if G is ω-bounded. This generalizes a theorem of Balcar and B laszczyk [1].

We prove the following theorems: 1. There exists an ω-covering with the property s0. 2. Under cov(N ) = 2 there exists X such that ∀B∈Bor[B ∩ X is not an ω-covering or X \B is not an ω-covering]. 3. Also we characterize the property of being an ω-covering.

1 Equipe Modèles de Calcul et Complexité Laboratoire de l’Informatique du Parallélisme CNRS et Ecole Normale Supérieure de Lyon 46, Allée d’Italie 69364 Lyon Cedex 07, France. [email protected] 2 Equipe d’Analyse Fonctionnelle Université Paris 6 4, place Jussieu, 75 252 Paris Cedex 05, France [email protected] and Université de Picardie, I.U.T. de l’Oise, site de Creil, 13, all...