关于具有σ几乎局部有限基的拓扑空间

In 1983, ML Ito and K.Tamano introduced the notion of almost locally finiteness and investigated some properties of the class of spaces with a σ almost locally finite base. In this paper, some more results about such spaces are given . The main results are as follows:( 1 ) The image of a space with a σ -almost locally finite base under the finite to one closed map has a σ-almost locally finite base;( 2 ) The locally finite sum theorem holds for such spaces;( 3 ) A space X has a σ almost locally finite base if and only if X is a paracompact σ space and every closed subset of X has an almost locally finite open neighborhood base; (4)The monotonically normal space with an M-structure has a a σalmost localiy finite base.     

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.     

Three-space problems for the bounded compact approximation property

In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p.     

THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.     

Finite groups whose maximal subgroups of sylow p-subgroups admit a p-solvable supplement

In this note,we show that if every maximal subgroup of a Sylow p-subgroup of a finite group has a p-solvable supplement then the group is necessarily p-solvable.This gives a positive answer to Problem 17.111 of the Kourovka Notebook(Unsolved Problems in Group Theory),which was posed by Skiba.     

SINGULAR INTEGRAL EQUATIONS IN ORLICZ SPACES (Ⅱ)

The singular integral equations with Cauchy kernels have studied in L_p(Γ),p>1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the completely continuous operator in the space sunder consideration. In this paper, we consider the equations mentioned above in Orlicz spaces L_M(Γ). It is proved that the Nether theorem and the index formula are hold true in the case of reflexive Orlicz spaces.     

A Theorem for Generalized Extension ofOperators and Some Applications

In this note it is shown that every bounded linear operator T Э B(Y,Z)defined on a closed subspace Y of a Banach space X admits a generalized extension T Э B(X, V). Some examples of the applications are given; especially, a characterization of H.I. spaces is obtained.     

EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES EQUIFOCAL HYPERSURFACES IN SYMMETRIC SPACES

1. IntroductionBy [111, a hypersurface in a symmetric space is called equifocal if every normal geodesicperpendiculajr to it is closed of constant length, say l, and contains Zg focal points for somepositive integer g. This is a natural generalization of isoparametric hypersurfaces in sphereswhere the illteger g is the number of distinct principal curvatures. In this note we considerequifocal hypersurfaces in simply connected rank one symmetric spaces, i.e. the complexprojective space CP", th…     

函数空间中的AP性质(英文)

In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C α (X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C α (X) is an AP-space which has countable tightness, then C α (X) is discretely generated.     

可解CN-群与π-可分Cππ-群

G. Higman studied first the finite groups in which every element has prime power order except 1(see[1]),that is,the centralizer of every element is is a p-group except 1.Later manv authors have generalized it. On the one hand, the generalization is CN-groups, that is, the finite groups in which the centralizer of every element is nilpotent except 1(see[2,3]).On the other hand, the generalization is C22-groups, that is, the groups are of even order and the centralizer of any involution is a 2-group;a C22-group named again CIT-gro-     

Division and k-th root theorems for Q-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f:K→X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X2 and X×[0,1] are Q-manifolds as well. We construct a countable familyχof spaces with DDP and cd-AP such that no space X∈χis homeomorphic to the Hilbert cube Q whereas the product X×Y of any different spaces X, Y∈χis homeomorphic to Q. We also show that no uncountable familyχwith such properties exists.     

闭序列覆盖映射的一些注记

In this paper, we mainly discuss the images of certain spaces under closed sequencecovering maps. It is showed that the property with a locally countable weak base is preserved by closed sequence-covering maps. And the following question is discussed： Are the closed sequence-covering images of spaces with a point-countable sn-network sn-first countable？     

PHASE-PORTRAIT OF A CERTAIN INTEGRABLE QUADRATIC DIFFERENTIAL SYSTEM WITH CENTER

In [1] we have proved that the quadratic differential system:has a center O(0, 0), which satisfies the last conditions of [2] 512 Theorem 12.3:Aside from O, (1) has a second finite critical point N(0, 1/n), it is an unstablenode. In [3], this is the case (7) in P.16, with bifurcation curve C12 in Fig.4.1and phase-portrait V32 in P.11.Now, put n = I, thenand (l) becomes:From [1] we know that (4) has a quadratic algebraic integral curveIt is a non--degenerate parabola with symetrical axis x…     

The Chevalley Groups G2(q) and Automorphisms of Linear Spaces

In this article we consider groups of automorphisms of flnite linear spaces that act prindtivelyon the lines. A finite linear space S consists of a set P of v points, together with a set L of bdistinguished subsets of P called lines, such that any two points lie on exactly one line. Supposethat a finite Iinear space S has a line-transitive subgroup, G, of automorphisms. Then everyline has the same number k of points and we call such a lineax space a regular linear space or a2 - (v, k, 1) de…     

List Vertex-arboricity of Planar Graphs without Intersecting 5-cycles

The vertex-arboricity a(G)of a graph G is the minimum number of colors required for a vertex coloring of G such that no cycle is monochromatic.The list vertex-arboricity al(G)is the list-coloring version of this concept.In this paper,we prove that every planar graph G without intersecting 5-cycles has al(G)≤2.This extends a result by Raspaud and Wang[On the vertex-arboricity of planar graphs,European J.Combin.29(2008),1064-1075]that every planar graph G without 5-cycles has a(G)≤2.     

Finite Groups in Which Each Irreducible Character has at Most Two Zeros

Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gG the conjugacy class of G containing element g. A well-known theorem of Burnside([1,Theorem 3.15]) states that every nonlinear X ∈ Irr(G) has a zero on G, that is, an element x (or a conjugacy class xG) of G with X(x) = 0. So, if the number of zeros of character table is very small, we may expect, the structure of group is heavily restricted. For example, [2, Proposition 2.7] claimes that G is a Frobenius group with a complement of order 2 if each row in charcter table has at most one zero (its proof uses the classification of simple groups). In this note, we characterize the finite group G satisfying the following hypothesis:     

Markov-modulated mean-variance problem for an insurer

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.     

CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES

This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.     

Almost simple groups with socle ~3D_4(q) act on finite linear spaces

After the classification of flag-transitive linear spaces, attention has now turned to line-transitive linear spaces. Such spaces are first divided into the point-imprimitive and the point-primitive, the first class is usually easy by the theorem of Delandtsheer and Doyen. The primitive ones are now subdivided, according to the O'Nan-Scotte theorem and some further work by Camina, into the socles which are an elementary abelian or non-abelian simple. In this paper, we consider the latter. Namely, T≤G≤Aut(T) and G acts line-transitively on finite linear spaces, where T is a non-abelian simple. We obtain some useful lemmas. In particular, we prove that when T is isomorphic to 3D4(q), then T is line-transitive, where q is a power of the prime p.     

THEORY OF SPECTRAL DECOMPOSITIONS WITH RESPECT TO THE IDENTITY FOR CLOSED OPERATORS

In this paper,the auther discusses some properties of closed operators acting on aBanach space with the spectral decomposition property with respect to the identity(abbrev.SDI).First,some equivalent conditions are given for a closed operator T to have the SDI.Next,for every hyperinvariant subspace Y of T with the SDI,it is proved that thecoinduced operator=T/Y has the SDI.Finally,properties of maximal nets of hyperinva-riant subspaces are discussed.