G-spaces and Fixed Point Sets

For a compact connected group G, in a compact free G-space M every closed subset is the fixed point set of an autohomeomorphism if the weight of M is not bigger than that of G. In a compact group with nonsingleton components, every closed subset is the fixed point set of an autohomeomorphism if and only if the weight of the whole group is not bigger than that of the component of the identity.     

A construction of classifying spaces for p-adic group actions

One major open problem in geometric topology is the Hilbert-Smith conjecture. A natural approach to this conjecture is to work on classifying spaces of p-adic integers. However, the well-known Milnor's construction of classifying space of p-adic integers is not locally connected, hence will not help to solve the conjecture, and the other known constructions are very complex. The goal of this paper is to give a new construction of classifying spaces for p-adic group actions.     

《泛函分析》中两个定理的教学与应用

本文讨论《泛函分析》中 Schauder不动点定理和 Arzela-Ascoli定理的教学方法并把它们用于互助生态模型得到两物种共存的一个充分条件 .     

偏序Menger PSM-空间中的耦合重合点定理

引入Menger概率S-度量空间的概念,研究其拓扑性质,基于混合g-单调映射的概念,在偏序Menger PSM-空间中,证明了自映象对满足?-压缩条件下的耦合重合点和耦合公共不动点定理和推论,并给出例子验证新结果的有效性.     

Menger概率度量空间中Caristi型混合不动点定理

本文在Menger概率度量空间中引进Caristi型混合不动点概念,得到两个混合不动点定理和两个集值映象序列的公共混合不动点定理,我们的定理改进和推广了Caristi不动点定理及相关的近期重要结果.     

Most standard spheres have smooth one fixed point actions ofA5. II

This paper proves that all standard spheresS ⁿ of dimension n=6 orn 9 have smooth one fixed point actions of the alternating groupA ₅ on five letters.Partially supported by the Yukawa Foundation, and also by Grant-in-Aid for Scientific Research 01740048.     

Fixed Point Theorems for Increasing Operators of None－continuity and None－compactness Conditions

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A new contraction principle in menger spaces

In the present work we introduce a new type of contraction mapping by using a specific function and obtain certain fixed point results in Menger spaces. The work is in line with the research for generalizing the Banach＇s contraction principle. We extend the notion of altering distance function to Menger Spaces and obtain fixed point results.     

PM-空间中混合压缩的不动点定理与重合点定理

引进了Menger PM-空间中多值情形下的相容映象和弱相容映象概念,并研究了二者之间的联系．在此基础上,获得了Menger PM-空间中若干新的不动点和重合点定理．最后,给出了这一结果在度量空间中的应用．     

Connectedness of Cone Superefficient Point Sets in Locally Convex Topological Vector Spaces

This paper studies the connectedness of the cone superefficient point set in locally convex topological vector spaces. First, we prove a scalarization theorem for a cone superefficient point set. From this result, we obtain the connectedness of a cone superefficient point set under the conditions that the set is cone convex and cone weakly compact.     

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.     

Chern and Pontryagin Numbers in Perfect Symmetries of Spheres

The paper presents a procedure for constructing smooth actions of finite perfect groups on spheres with fixed point sets having certain prescribed properties (Theorem A); in particular, having any prescribed configuration of Chern and Pontryagin numbers (Corollary C). The main ingredients used are equivariant thickening and equivariant surgery.     

一类混合单调算子的耦合不动点定理及其应用

讨论了一类混合单调算子的耦合不动点定理,并获得了最大最小耦合不动点.作为应用,讨论了Banach空间中含有不连续项的混合单调Volterra型积分方程耦合拟解的存在性问题.     

On Finite Groups Acting on Contractible Complexes of Dimension Two

We show that every action of a finite group on a one-connected diagrammatically reducible two-complex has a fixed point. The proof makes use of Stallings' notion of foldings of graphs, appropriately adapted to a certain two-dimensional setting.