A remark on the homomorphism on

Let be a real compact space. Without using the axiom of choice we present a simple and direct proof that a non-zero homomorphism on is determined by a point.

     

Strong pseudo-contractions perturbed by compact operators in Banach spaces

Let be a (real) Banach space, let be an open subset of , and let denote the collection of all nonempty bounded and closed subsets of . Suppose is continuous from into with respect to the Hausdorff metric and strongly pseudo-contractive, while is compact from into . Then has a fixed point if it satisfies the classical Leray-Schauder condition on the boundary of .

     

A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold

In this paper, we construct a non-toral compact complex parallelizable pseudo-Kähler solvmanifold.pseudo-Kähler, complex-parallelizable manifold, compact solvmanifold, Borel–Remmert theorem.Mathematics Subject Classiffications (2000). 53C15, 53D05     

On the Algebra of Pair Integral Operators with Homogeneous Kernels

In this paper, we study the Banach algebra generated by multidimensional pair integral operators with homogeneous kernels. We describe necessary and sufficient conditions for operators from the algebra to be Fredholm and present a formula for calculating the index.     

On Fredholm Operators Between Non-archimedean Fréchet Spaces

It is proved that the index of a Fredholm operator between non-Archimedean Fréchet spaces is preserved under compact perturbations. A similar result is shown for Fredholm operators between non-Archimedean polar regular LF-spaces.     

On the Weight of Nowhere Dense Subsets in Compact Spaces

We study a new cardinal-valued invariant ndw(X) (calling it the nd-weight of X) of a topological space which is defined as the least upper bound of the weights of nowhere dense subsets of X. The main result is the proof of the inequality hl(X)ndw(X) for compact sets without isolated points ((hl is the hereditary Lindelof number). This inequality implies that a compact space without isolated points of countable nd-weight is completely normal. Assuming the continuum hypothesis, we construct an example of a nonmetrizable compact space of countable nd-weight without isolated points.     

Hemiring-homomorphisms,Stone Čech Compactification and Hewitt Realcompactification

In this paper the Stone-ech Compactification and Hewitt Realcompactification of a Tychonoff space X are shown as the spaces of Hemiring Homomorphisms from the hemirings C^*₊(X) and C₊(X) to IR₊ respectively.AMS Subject Classification: 2000, 54E25     

Explicit Expressions for Timelike and Spacelike Observables of Quantum Chromodynamics in Analytic Perturbation Theory

We study the possibility of expressing the invariant QCD coupling function (i.e., the effective coupling constant) in an explicit analytic form in two- and three-loop approximations as well as in the case of the Padé-transformed -function. Both the timelike and spacelike domains are investigated. Technical aspects of the Shirkov–Solovtsov analytic perturbation theory are considered. Explicit expressions for the two- and three-loop effective coupling functions in the timelike domain are obtained. In the last case, we apply a new method of expanding functions represented in an arbitrary loop order of perturbation theory in powers of the two-loop function. The comparison with numerical data in the infrared region shows that the obtained explicit expressions for the three-loop functions agree fully with the exact numerical results.     

Actions of Finite Hypergroups

This paper is concerned with actions of finite hypergroups on sets. After introducing the definitions in the first section, we use the notion of maximal actions to characterise those hypergroups which arise from association schemes, introduce the natural sub-class of *-actions of a hypergroup and introduce a geometric condition for the existence of *-actions of a Hermitian hypergroup. Following an insightful suggestion of Eiichi Bannai we obtain an example of the surprising phenomenon of a 3-element hypergroup with infinitely many pairwise inequivalent irreducible *-actions.     

A proof of the Generalized Banach Contraction Conjecture

We introduce the notion of -continuity, which generalizes both continuity and the hypothesis in the Generalized Banach Contraction Conjecture, and prove that any -continuous self-map on a scattered compact space, has an invariant finite set. We use the results and the techniques to prove the Generalized Banach Contraction Conjecture.