Topological algebraic structure on Souslin and Aronszajn lines

Z. Feng and R.W. Heath proved that any separable linearly ordered space (LOTS) which is a cancellative topological semigroup must be metrizable. In this note, we show that the same holds more generally for CCC LOTS by proving that no Souslin line admits a continuous cancellative binary operation. We also show that no Lindelöf Aronszajn line admits such an operation.     

Strongly essential coalitions and the nucleolus of peer group games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespecified collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n−1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2ⁿ⁻¹. We propose an algorithm that computes the nucleolus of an n-player peer group game in time directly from the data of the underlying peer group situation.Research supported in part by OTKA grant T030945. The authors thank a referee and the editor for their suggestions on how to improve the presentation     

On group operations on homogeneous spaces

It is proved that every countably infinite homogeneous regular space admits a structure of any countably infinite group with continuous left shifts.

     

Locale的弱拓扑表达

本文引入了弱拓扑空间的概念,证明了locale范畴与弱拓扑空间范畴的关系类似于拓扑空间范畴与locale范畴的关系。locale范畴严格包含于弱拓扑空间范畴并且与Sober的弱拓扑空间范畴等价。     

拓扑群在连续统上的膨胀作用

本文把一个同胚的膨胀作用推广到拓扑群的情形,并研究了有限生成离散群 的膨胀作用,得到了如下结果:Z×Z不能膨胀地作用在单位闭区间I上,而自由积 Z★Z可以膨胀地作用在I上.     

Topological Hypergroups in the Sense of Marty

In this paper, we introduce the concept of topological hypergroups as a generalization of topological groups. A topological hypergroup is a nonempty set endowed with two structures, that of a topological space and that of a hypergroup. Let (H, ○) be a hypergroup and (H, τ) be a topological space such that the mappings (x, y) → x ○ y and (x, y) → x/y from H × H to 𝒫*(H) are continuous. The main tool to obtain basic properties of hypergroups is the fundamental relation β*. So, by considering the quotient topology induced by the fundamental relation on a hypergroup (H, ○) we show that if every open subset of H is a complete part, then the fundamental group of H is a topological group.

It is important to mention that in this paper the topological hypergroups are different from topological hypergroups which was initiated by Dunkl and Jewett.     

子流形与拓扑球面定理

本文建立了球面Sn p(c) (c>0 )中的完备子流形的一个拓扑球面定理 ,结果表明完备子流形的拓扑是受其内在和外在曲率不变量满足的某些条件所影响的     

拓扑空间范畴、拓扑FUZZ范畴与拓扑分子格范畴间的反射与余反射

从整体角度出发，证明了拓扑空间范畴Ｔｏｐ分别是拓扑Ｆｕｚｚ范畴ＴｏｐＦｕｚ与拓扑分子格范畴ＴＭＬ的反射与余反射满子范畴，ＴｏｐＦｕｚ是ＴＭＬ的反射与余反射（非满）子范畴．     

Topological degree and number of Nash equilibrium points of bimatrix games

In this paper, using the topological degree, we give a new proof of a well-known result: the number of Nash equilibrium points of a nondegenerate bimatrix game is odd. The calculation of the topological degree allows the localization of the whole set of non-degenerate equilibrium points.     

Three-Dimensional Topological Loops with Solvable Multiplication Groups

We prove that each 3-dimensional connected topological loop L having a solvable Lie group of dimension ≤5 as the multiplication group of L is centrally nilpotent of class 2. Moreover, we classify the solvable non-nilpotent Lie groups G which are multiplication groups for 3-dimensional simply connected topological loops L and dim G ≤ 5. These groups are direct products of proper connected Lie groups and have dimension 5. We find also the inner mapping groups of L.     

Normal Domain Representations of Topological Spaces

D′ ⊆ D is a normal totality on a Scott domain D if it is upward closed and x ⊓ y ∈ D′ is an equivalence relation on D′. We prove that every topological space can be represented by a domain with norma totality.     

Weak selections and pseudocompactness

We prove that every pseudocompact space that admits a weak selection is sequentially compact.

     

Topological centers of certain dual algebras

Let be a Banach algebra with a bounded approximate identity. Let and be, respectively, the topological centers of the algebras and . In this paper, for weakly sequentially complete Banach algebras, in particular for the group and Fourier algebras and , we study the sets , , the relations between them and with several other subspaces of or .

     

Sequential group topology on rationals with intermediate sequential order

Using CH we construct a countable sequential topological group whose sequential order is between and giving a consistent negative answer to P. Niykos' question.

     

Topological vector spaces admissible in economic equilibrium theory

In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space.     

On the continuity of the evaluation mapping associated with a group and its character group

For an abelian Hausdorff group , let denote the character group endowed with the compact-open topology and let denote the canonical homomorphism. We show that the evaluation mapping from into the torus is continuous if and only if is locally compact and is continuous. If is injective and open, then the evaluation mapping is continuous if and only if is locally compact. Several examples and counterexamples are given.

     

On the Reflectivity and Coreflectivity of L-Fuzzifying Topological Spaces in L-Topological Spaces

In this paper it is proved that for all completely distributive lattices L, the category of L-fuzzifying topological spaces can be embedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory. Received April 2, 1999, Revised January 31, 2000, Accepted February 2, 2000     

序列伪轨跟踪性与拓扑可迁

给出序列伪轨跟踪性的定义,得到拓扑可迁的一个充分条件,并证明,若f是同胚,则f具有序列伪轨跟踪性当且仅当其逆极限空间上的移位映射σf具有序列伪轨跟踪性。     

连续自映射拓扑压的两个注记

令T:X→ X是紧度量空间(X,d)上的连续映射.该文给出了T的拓扑压和T在非游荡集上的限制的拓扑压相等的不依赖于变分原理的一个直接证明.同时,还讨论了半共轭的两个系统的拓扑压之间的关系,证明了拓扑压在一致有限对一条件下是半共轭不变量.