The goal of this paper is to find the "Lie groups" for three well-known Lie algebras: the globally Hamiltonian vector fields, the infinitesimal quantomorphisms and the homogeneous real-valued functions of degree one on the cotangent bundle minus the zero section. In all our considerations the underlying manifold is assumed to be compact without boundary. Before explaining and motivating our res...

in this paper, vector ultrametric spaces are introduced and a fixed point theorem is given forcorrespondences. our main result generalizes a known theorem in ordinary ultrametric spaces.

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

Let p : E−→B be a principal bundle with fibre and structure group the torus T ∼ = (C *) n over a topological space B. Let X be a nonsingular projective T-toric variety. One has the X-bundle π : E(X)−→B where E(X) = E × T X, π([e, x]) = p(e). This is a Zariski locally trivial fibre bundle in case p : E−→B is algebraic. The purpose of this note is to describe (i) the singular cohomology ring of E...

An account of the Schwartz space of rapidly decreasing functions as a topological vector space with additional special structures is presented in a manner that provides all the essential background ideas for some areas of quantum mechanics along with infinite-dimensional distribution theory.

J. Dobrakovová and the author in [7] introduced the relation of nearness in Banach space. In this paper we will go on investigating the nearness relation in a linear space with a countable vector base, focusing the results to topological properties of such relations.

Integral calculus on the space A/G of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of A/G. The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the mea...

We study mixing properties (topological mixing and weak mixing of arbitrary order) for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. The type of nonautonomous systems considered here can be defined by a sequence (Ti)i∈N of linear operators Ti : X → X on a topological vector space X such that there is an invariant set Y for which...

A systematic analysis is made of the character of the free and free abelian topological groups on uniform spaces and on topological spaces. In the case of the free abelian topological group on a uniform space, expressions are given for the character in terms of simple cardinal invariants of the family of uniformly continuous pseudometrics of the given uniform space and of the uniformity itself....