Totally Bounded Quasi-Uniformities and Pseudocompactness of Bispaces

 We characterize pairwise Tychonoff bispaces that admit only totally bounded quasi-uniformities in terms of a suitable notion of bitopological pseudocompactness. We also show that a pairwise Tychonoff bispace has a unique (up to equivalence) bicompactification if and only if it admits a unique totally bounded quasi-unifomity. These results extend classical theorems of R. Doss for uniform spaces to the quasi-uniform (bitopological) setting, and are applied to the study of T ₀ topological spaces that admit a unique quasi-uniformity and a unique bicompactification, respectively. Finally, we discuss the problem of extending the classical Glicksberg theorem on product of pseudocompact spaces to bispaces and a partial solution is obtained. Supported by the Spanish Ministry of Science and Technology, grant BFM2000-1111. Supported by a grant from Generalitat Valenciana. Received November 7, 2001; in revised form August 14, 2002     

The Number of Compatible Totally Bounded Quasi-Uniformities

We prove that a topological space that admits a nontransitive totally bounded quasi-uniformity, admits at least nontransitive totally bounded quasi-uniformities. Furthermore we show that each infinite T ₂-space admits at least transitive totally bounded quasi-uniformities. In fact, each supersober space having a discrete subspace of infinite cardinality admits at least transitive totally bounded quasi-uniformities.     

完全分配格上的全有界一致结构与邻近结构

本文的目的是在具有逆序对合对应的完全分配格上研究点式（拟）一致结构与（拟）邻近中构的联系,证明了在全有界点式一致结构与邻近结构间存在一个一一对应关系。     

Precompact abelian groups and topological annihilators

For a compact Hausdorff abelian group K and its subgroup H≤K, one defines the g-closureg_K(H) of H in K as the subgroup consisting of χ∈K such that χ(a_n)?0 in T=R/Z for every sequence {a_n} in (the Pontryagin dual of K) that converges to 0 in the topology that H induces on . We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the paper are used to construct a close relative of the closure operator g that coincides with the G_δ-closure on compact Hausdorff abelian groups, and thus captures realcompactness and pseudocompactness of subgroups.     

Holomorphic Retractions of Bounded Symmetric Domains onto Totally Geodesic Complex Submanifolds

Given a bounded symmetric domain Ω the author considers the geometry of its totally geodesic complex submanifolds S ? Ω.In terms of the Harish-Chandra realization Ω and taking S to pass through the origin 0 ∈Ω,so that S=E ∩Ωfor some complex vector subspace of Cⁿ,the author shows that the orthogonal projectionρ:Ω→ E maps Ω onto S,and deduces that S?Ω is a holomorphic isometry with respect to the Caratheodory metric.His first theorem gives a new derivation of a result of Yeung’s deduced...     

Existence and Number of Maximal Precompact Topologies on Abelian Groups

The lattice PC(G) of precompact group topologies on an Abelian group G is isomorphic with the lattice SG(G*) of subgroups of the algebraic character group (Remus, 1983). Remus used this result to determine the number of precompact [Hausdorff] topologies on Abelian groups. In this paper the same tool is applied to the problems of existence and number of maximal precompact [Hausdorff] topologies on an Abelian group G, i.e. antiatoms in the lattice PC(G). It is shown that PC(G) has antiatoms iff G is not torsion-free. Further the number of maximal precompact [Hausdorff] topologies is expressed in terms of the cardinalities of the p-components of the group G.     

Bounded geometry,growth and topology

We characterize functions which are growth types of Riemannian manifolds of bounded geometry.     

Bounded rationality, strategy simplification, and equilibrium

It is frequently suggested that predictions made by game theory could be improved by considering computational restrictions when modeling agents. Under the supposition that players in a game may desire to balance maximization of payoff with minimization of strategy complexity, Rubinstein and co-authors studied forms of Nash equilibrium where strategies are maximally simplified in that no strategy can be further simplified without sacrificing payoff. Inspired by this line of work, we introduce a notion of equilibrium whereby strategies are also maximally simplified, but with respect to a simplification procedure that is more careful in that a player will not simplify if the simplification incents other players to deviate. We study such equilibria in two-player machine games in which players choose finite automata that succinctly represent strategies for repeated games; in this context, we present techniques for establishing that an outcome is at equilibrium and present results on the structure of equilibria.     

Bounded Sequences,Orbits and Invariant Subspaces

Let {x _n } be a sequence of complex numbers and let \({\Delta^nx_j = \sum\nolimits_{k=0}^{n} (-1)^k\break\left(\begin{array}{l}n\\ k\\\end{array} \right)x_{n-k+j}}\) . In this paper, we will show that if \({ |x_n| = O(n^k)}\) , as n → ∞ for some positive integer k, and \({n|\Delta^n x_j|^{\frac{1}{n}} \to 0}\) as n→ ∞, then \({\Delta^{k+1} x_j = 0}\) . More importantly, applications to the orbits of operators and invariant subspace problem are also given; this helps to improve former results obtained by Gelfand–Hille, Mbekhta–Zemánek and others.     

Curvature, Diameter and Bounded Betti Numbers

In this paper, we introduce the notion of bounded Betti numbers, and show that the bounded Betti numbers of a closed Riemannian n-manifold (M, g) with Ric (M) ≥ -(n - 1) and Diam (M) ≤ D are bounded by a number depending on D and n. We also show that there are only finitely many isometric isomorphism types of bounded cohomology groups (H*(M), || · ||∞) among closed Riemannian manifold (M, g) with K(M) ≥-1 and Diam (M) ≤ D.     

Totally real bisectional curvature,Bochner-Kaehler and Einstein-Kaehler manifolds

By studying various curvature properties of Kaehler manifolds, we establish many new simple geometric characterizations of Bochner-Kaehler and Einstein-Kaehler spaces and of complex space forms.     

Bounded Laplace transforms,primitives and semigroup orbits

Let $f : \mathbb{R}_{+} \rightarrow \mathbb{C}$ be an exponentially bounded, measurable function whose Laplace transform has a bounded holomorphic extension to the open right half-plane. It is known that there is a constant C such that $\mid \int\limits^t_0 f(s) ds \mid\, \leq C (1 + t)$ for all $t \geq 0$. We show that this estimate is sharp. Furthermore, the corresponding estimates for orbits of $C_0$-semigroups are also sharp. Received:17 January 2001; revised manuscropt accepted: 8 February 2001     

Lipeomorphisms, Sets of Bounded Variation and Integrals

To obtain a lipeomorphic (bi-Lipschitz) change of variables theorem for generalized integrals lipeomorphic transformations of partitions are studied.     

Bounded variable logics: two, three, and more

Consider the bounded variable logics (with k variable symbols), and (with k variables in the presence of counting quantifiers ). These fragments of infinitary logic are well known to provide an adequate logical framework for some important issues in finite model theory. This paper deals with a translation that associates equivalence of structures in the k-variable fragments with bisimulation equivalence between derived structures. Apart from a uniform and intuitively appealing treatment of these equivalences, this approach relates some interesting issues for the case of an arbitrary number of variables to the case of just three variables. Invertibility of the invariants for , in particular, would imply a positive answer to the tempting conjecture that fixed-point logic with counting captures Ptime . Received July 13, 1996     

Separation of Sets,Lagrange Multipliers,and Totally Regular Extremum Problems

We introduce the concept of total regularity for the separation of sets, and we give a characterization of it. Also, we prove the equivalence between total regularity and boundedness of the generalized multipliers associated to the separation, and we compute the value of the bound. Then, we give a theorem concerning the uniqueness of such multipliers. Afterward, the previous results are applied to the study of the impossibility of generalized systems; particular attention is devoted to systems arising from the optimality conditions of constrained extremum problems.     

Totally Splittable Polytopes

A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a complete classification of the totally splittable polytopes.     

Totally smooth renormings

Archiv der Mathematik - We study the problem of totally smooth renormings of Banach spaces and provide such renormings for spaces which are weakly compactly generated. We also consider renormings...