Lawson紧的代数L-domain递归方程的逻辑形式

本文的目的是为Lawson紧的代数L-domain递归方程及其解提供一种逻辑刻画。基于N-序列演算上的子系统关系,证明了N-序列演算之集是定向完备的,并在这一定向完备偏序集上引入了三种连续构造算子：提升,联结和以及分离和。从而求解domain结构递归方程的问题可归结为如何构建连续映射的不动点。     

局部强紧空间的Hoare空间与Smyth空间

本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.     

可数强F紧集的刻画与性质

借助α-ω聚点与α-聚点概念给出可数强F紧集的两个刻画定理,进而讨论可数强F紧集在L值Zadeh型函数下的逆不变性,证明了可数强F紧集与强F紧集的乘积是可数强F紧的。     

强S-仿紧空间

在一般拓扑空间中给出了强S-仿紧空间的概念,研究了它的性质并给出了Hausdorff空间下它的等价刻画,同时讨论了它的相对性质.     

L-拓扑空间的弱局部强F紧性及单点强F紧化

以R.Lowen的强F紧性为基础,定义了L-拓扑空间的弱局部强F紧性及单点强F紧化,推广了有关弱局部紧拓扑空间和拓扑空间的单点紧化的若干结果,证明了L-拓扑空间的弱局部强F紧性是拓扑空间的弱局部紧性的L-推广。     

信息代数紧扩张的一种新方法

本文研究了从一般信息代数获取紧信息代数的一种新方法.通过在一个信息代数的定向集族上建立一个等价关系,证得相应的等价类全体之集关于联合和聚焦两种运算构成了原信息代数的一个紧扩张.     

关于Scott开滤子拓扑的core紧性

本文讨论了那样一些ＤＣＰＯ（即定向完备偏序集）的刻划问题,它们在赋以Ｓｃｏｔｔ开滤子拓扑后,其拓扑空间的开集格是连续格。该问题也是由ＬａｗｓｏｎＪＤ。与ＭｉｓｌｏｖｅＭ．提出的一系列公开问题中的一个［１］。     

连续信息代数

给出基于自由域信息代数和带论域信息代数上的连续性概念.证明在城集格有最大元的情况下,两种连续性之间是相互对应的.定义了连续信息代数之间的连续映射的概念,证得:若(φ,D),(ψ,E)都是强连续的信息代数.则([φ→ψ]c,D×E)也是强连续的.     

强1-星紧空间的性质

探讨强1-星紧与可数紧、feebly紧、伪紧和DFCC之间的关系，给出它在具有分离性（Q）的T1空间类中的特征．     

紧对称空间上Riesz平均的强逼近

本文在紧对称空间中给出了全测度集上Ｒｉｅｓｚ平均强逼近的阶     

Continuous L-domains in logical form

We introduce a framework of approximable disjunctive propositional logic, which is the logic that results from a disjunctive propositional logic by adding an additional connective. The Lindenbaum algebra of this logic is an approximable dD-algebra. We show that for any approximable dD-algebra, its approximable filters ordered by set inclusion form a continuous L-domain. Conversely, every continuous L-domain can be represented as an approximable dD-algebra. Moreover, we establish a categorical equivalence between the category of approximable dD-algebras with approximable dD-algebra morphisms and that of continuous L-domains with Scott-continuous functions. This extends Abramsky's Domain Theory in Logical Form to the world of continuous L-domains. As an application, we give an affirmative answer to an open problem of Chen and Jung.     

Strong characterizing sequences for subgroups of compact groups

In [A. Biró, V.T. Sós, Strong characterizing sequences in simultaneous Diophantine approximation, J. Number Theory 99 (2003) 405–414] we proved that if Γ is a subgroup of the torus R/Z generated by finitely many independent irrationals, then there is an infinite subset AZ which characterizes Γ in the sense that for γR/Z we have ∑_aAaγ<∞ if and only if γΓ. Here we consider a general compact metrizable Abelian group G instead of R/Z, and we characterize its finitely generated free subgroups Γ by subsets AG^*, where G^* is the Pontriagin dual of G. For this case we prove stronger forms of the analogue of the theorem of the above mentioned work, and we find necessary and sufficient conditions for a kind of strengthening of this statement to be true.     

模糊星形数空间在L_p度量下的紧集刻画

1990年,P.Diamond首次给出了由全体相对于原点的模糊星形数构成的空间在Lp度量下的紧集刻画。后来,Congxin Wu和Zhitao Zhao通过一个反例指出了P.Diamond的刻画是不正确的,并给出了一种正确的刻画。在这篇文章中,我们将进一步推广这个结论,得到了全体模糊星形数空间在Lp度量下的紧集刻画。     

Compact quantum metric spaces and ergodic actions of compact quantum groups

We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T→EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if and only if the function counting the multiplicity of γ in each fibre is continuous over T for every equivalence class γ of irreducible unitary representations of G. Generalizations for arbitrary compact quantum groups are also obtained. In the case G is a compact group, the restriction of this topology on the subset of isomorphism classes of ergodic actions of full multiplicity coincides with the topology coming from the work of Landstad and Wassermann. Podle? spheres are shown to be continuous in the natural parameter as ergodic actions of the quantum SU(2) group. We also introduce a notion of regularity for quantum metrics on G, and show how to construct a quantum metric from any ergodic action of G, starting from a regular quantum metric on G. Furthermore, we introduce a quantum Gromov-Hausdorff distance between ergodic actions of G when G is separable and show that it induces the above topology.     

Compact adjoint operators and approximation properties

This paper is concerned with the space of all compact adjoint operators from dual spaces of Banach spaces into dual spaces of Banach spaces and approximation properties. For some topology on the space of all bounded linear operators from separable dual spaces of Banach spaces into dual spaces of Banach spaces, it is shown that if a bounded linear operator is approximated by a net of compact adjoint operators, then the operator can be approximated by a sequence of compact adjoint operators whose operator norms are less than or equal to the operator norm of the operator. Also we obtain applications of the theory and, in particular, apply the theory to approximation properties.     

Algebraic Characterization of Dense-Separability Among Compact Spaces

In this note, we show that a compact Hausdorff space X is dense-separable if and only if every family of ideals of C(X) with zero intersection has a countable subfamily with zero intersection. As a consequence of this characterization we observe that every compact dense-separable space whith Soc(C(X)) = 0 has a countable dense and co-dense subset.     

Algebraic shifting of strongly edge decomposable spheres

Recently, Nevo introduced the notion of strongly edge decomposable spheres. In this paper, we characterize algebraic shifted complexes of those spheres. Algebraically, this result yields the characterization of the generic initial ideal of the Stanley-Reisner ideal of Gorenstein^∗ complexes having the strong Lefschetz property in characteristic 0.     

A Covering Space with No Compact Core

This note describes an example of a compact aspherical 2-complex X with a covering space , such that is finitely presented but has no compact core.I thank John Stallings for being my 'Senior Scientist' in 1996–1997, and for many superimaginative e-mails that led to this relationship.     

Algebraic curves and maximal arcs

A lower bound on the minimum degree of the plane algebraic curves containing every point in a large point-set of the Desarguesian plane PG(2,q) is obtained. The case where is a maximal (k,n)-arc is considered in greater depth. Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni.