Rings of quotients of C(X) induced by points

We study two rings of quotients of C(X), the ring of continuous functions on the Tychonoff space X. The first, F(X), is the ring of quotients induced by the filter of ideals consisting of dense finite intersections of fixed maximal ideals. The second, C[F], is the ring of quotients induced by the filter of dense cofinite subspaces of X. After some preliminary information we explicitly describe in §2 and §3 the constructions of these rings of quotients. In the third section, we use F(X)and C[F] to define and study the class of h-points and h-spaces. In particular, we show that C-spaces and P-spaces are h-spaces. In the last section we construct an ideal of C(X)which will be used to give an ideal theoretic characterization of h-points. This revised version was published online in June 2006 with corrections to the Cover Date.     

On quasi-Souslin C c (X) spaces

We prove that the space C _c (X) of the real-valued continuous functions with the compact-open topology is quasi-Souslin iff it is K-analytic. This implies that C _c (X) is K-analytic iff it is dominated by the irrationals. Partially supported by the project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder projects).     

The dual of C ps (X)

This is a study of the dual space of continuous linear functionals on the function space C_ps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.      

Ck（X）的扇密度和强Frechet性质

本文证明了如下两个定理：（１）Ｃ＿ｋ（Ｘ）为强Ｆｒｅｃｈｅｔ空间（或者Ｆｒｅｃｈｅｔ空间）的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝，存在Ｕ＿ｎ∈ｕ＿ｎ，使｛Ｕ＿ｎ：ｎ∈Ｎ｝为Ｘ的Ｋ－序列，（２）Ｃ＿ｋ（Ｘ）有可数扇密度的充分必要条件是Ｘ中的每一开Ｋ－覆盖序列｛ｕ＿ｎ：ｎ∈Ｎ｝存在ｕ＿ｎ的有限于族ｕ＇＿ｎ，使｛ｕ＇＿ｎ：ｎ∈Ｎ｝是Ｘ的开Ｋ－覆盖．     

作用在有限线性空间上基柱为F_4(q)的几乎单群

线传递线性空间可以分为非点本原和点本原两种情形,而点本原的情况又可以分成基柱为初等交换群或非交换单群两种情形.本文考虑后一种情形,即T是非交换单群,T≤G≤Aut(T)且G线传递,点本原作用在有限线性空间上的情形.证明了当T同构于F_4(q)时,若T_L不是~2F_4(q),B_4(q),D_4(q).S_3,~3D_4(q).3,F_4(q~(1/2))和T的抛物子群的子群时,T也是线传递的,这里q是素数p的方幂.     

The Non—standard Characteristics of Functional Spaces K（X） and C0（X）

ＬｅｔＵｂｅａｓｔａｎｄａｒｄｕｎｉｖｅｒｓｅａｎｄＵｂｅａｎｅｎｌａｒｇｅｄｎｏｎｓｔａｎｄａｒｄｕｎｉｖｅｒｓｅｗｉｔｈｒｅｓｐｅｃｔｔｏＵ．ＸｉｓａｔｏｐｏｌｏｇｉｃａｌｓｐａｃｅｗｈｉｃｈｉｎｃｌｕｄｅｄｉｎｔｈｅｉｎｄｉｖｉｄｕａｌｓｅｔｏｆＵ，ｔｈａｔｉｓ，ＸＸ．Ｄｅｆｉｎｉｔｉｏｎ１　Ｆｏｒｅａｃｈｘ∈Ｘ，ｗｅｄｅｆｉｎｅｍ（ｘ）＝∩｛Ｖ：Ｖ∈Ｉｘ｝ａｎｄｃａｌｌｍ（ｘ）ｔｈｅｍｏｎａｄｏｆｘ（Ｉｘｉｓｔｈｅｏｐｅｎｎｅｉｇｈｂｏｒｈｏｏｄｏｆｘ）．Ｗｅｗｒｉｔｅｙ≈ｘｆｏ…     

On operations in C(X) determined by continuous functions

Let C(X) be the space of all continuous real-valued functions on a compact topological space. Then every continuous function $\varphi: {\mathbb{R}^{2}\to \mathbb{R}}$ defines an operation Φ:C(X)×C(X)→C(X), Φ(f,g)(x)=φ(f(x),g(x)) for x∈X. We show some sufficient and some necessary conditions for the openness and the weak openness of Φ.     

A criterion of SNT(X) = {[X]} for hyperformal spaces

We will give a condition characterizing spaces X with SNT(X) = {[X]} which generalizes the corresponding result of McGibbon and Moller [8] for rational H-spaces.      

Zero-divisor graph of C(X)

Summary In this article the zero-divisor graph Γ(C(X)) of the ring C(X) is studied. We associate the ring properties of C(X), the graph properties of Γ(C(X)) and the topological properties of X. Cycles in Γ(C(X)) are investigated and an algebraic and a topological characterization is given for the graph Γ(C(X)) to be triangulated or hypertriangulated. We have shown that the clique number of Γ(C(X)), the cellularity of X and the Goldie dimension of C(X) coincide. It turns out that the dominating number of Γ(C(X)) is between the density and the weight of X. Finally we have shown that Γ(C(X)) is not triangulated and the set of centers of Γ(C(X)) is a dominating set if and only if the set of isolated points of X is dense in X if and only if the socle of C(X) is an essential ideal.     

格值命题逻辑LP(X)中不可分极简式的性质

基于格值命题逻辑LP(X)的α-归结原理及α-归结自动推理方法，能够较好地刻画具有可比较性和不可比较性的不确定性信息。LP(X)中的不可分极简式是一个非常重要的概念，本文对蕴涵运算个数小于3的不可分极简式的性质和判定方法进行了讨论，得到了一些重要结论。     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

A Note on $Card(X)$

The main interests here are to study the relationship between $card(X)$ and $card({\cal P}(X))$ and the connection between the separability of a space $X$ and cardinality of some function space on it. We will convert the calculation of $card({\cal P}(X))$ to the calculation of $card({\cal F}(X\rightarrow Q))$.The main tool we used here is Zorn Lemma.     

Conditions on Normal Spaces of Finite Rank That Guarantee C(X) is SV

An f-ring A is an SV f-ring if for every minimal prime ?-ideal P of A, A/P is a valuation domain. A topological space X is an SV space if C(X) is an SV f-ring. For normal spaces, several conditions are shown to guarantee the space is an SV space. For example, a normal space of finite rank for which the closure of the set of points of rank greater than 1 is an F-subspace, is an SV space. For normal spaces of rank 2, a characterization of SV spaces is given.     

Algebras between C *(X) and C(X) that are closed under countable composition

Let be the algebra of all real-valued continuous functions on a completely regular space X, and the subalgebra of bounded functions. We show that the space of real maximal ideals of an intermediate algebra between and is a -embedded closed subspace of the product of with a product of copies of the real line. We make use of this embedding to provide a new characterization of the intermediate algebras that are closed under countable composition, and to exhibit an example of an intermediate algebra on that is closed under countable composition but not isomorphic to any .     

SOME PROPERTIES OF Λω^p（X,μ）

In this paper, we shall give a necessary and sufficient condition for which the dual of Λ _ω ^p (X, M, μ) (0<p<∞) is zero, and a necessary and sufficient condition for which Λ _ω ^p (X, M, μ), (0<p<1) is normable. Supported by 973 project (G1999075105), RFDP (20030335019) and ZJNSF(RC97017).     

Matrix transformations of lq（X） to lP（Y）

Let X and Y be Banach spaces,0 ＜ q ＜ +∞,1 ＜ p ＜ +∞.In this paper,we characterize matrix transformations of lq(X) to lp(Y).     

C(X) in the weak topology

Some relations between cardinal invariants ofX andC(X) are established in the weak topology, whereC(X) is the space of continuous real-valued functions onX in the compact-open topology.