A Serre-Swan Theorem for Bundles of Topological Modules

Let R be a unital topological ring whose set of invertible elements is open and inversion is continuous, and let X be a compact Hausdorff space admitting continuous R-valued partitions of unity. Considering bundles over X of fibre type a projective finitely generated R-module, we prove a Serre-Swan type theorem: namely, the category of these bundles is equivalent to the category of projective finitely generated modules over the ring of continuous R-valued functions on X.     

Hermitian Metric Rigidity for Foliated Vector Bundles

We show that the canonical isometric imbedding of the symplectic group Sp(n) into R⁴n² gives the least-dimensional isometric imbedding into the Euclidean space, even in the local standpoint. We prove this result by calculating the quantity p_G determined by the curvature of Sp(n), which serves as an obstruction to the existence of local isometric imbeddings. We also exhibit the estimates on the value p_G for the remaining compact classical simple Lie groups, and improve the previous results on the codimension of local isometric imbeddings of these groups.     

A Liouville-Type Theorem for Smooth Metric Measure Spaces

For smooth metric measure spaces (M,g,e ^?f d _vol ) we prove a Liouville-type theorem when the Bakry–Emery Ricci tensor is nonnegative. This generalizes a result of Yau, which is recovered in the case f is constant. This result follows from a gradient estimate for f-harmonic functions on smooth metric measure spaces with Bakry–Emery Ricci tensor bounded from below.     

A Metric Version of Milyutin Theorem

Open covering and metric regularity are properties playing a crucial role in several topics of modern variational analysis. Here their stability behaviour in the presence of perturbations is investigated in a purely metric setting. Some results in this sense are obtained, which lead to extend the known Milyutin theorem, and then to expand the concept of radius of regularity, a quantitative measure of the open covering stability. Estimations for the latter in terms of covering moduli are provided.     

A Combination Theorem for Relatively Hyperbolic Groups

Given a graph of -hyperbolic spaces, this paper gives sufficientconditions that ensure that the graph itself is -hyperbolic.As an application, a simple proof is given to show that limitgroups are relatively hyperbolic. 2000 Mathematics Subject Classification57M07, 20F65.     

An Index Theorem on Foliated Flat Bundles

In this paper we shall study the indices of some leafwise elliptic operators on foliated bundles, by using some concretely constructed cyclic cocycles on the smooth foliation algebras. The key is a decomposition of the KK-classes associated to the operators. The group action analogue of this approach provides a bridge from the classical Atiyah-Singer index theorem to the higher -index theorem of Connes and Moscovici.     

P-平均对称差度量的收敛定理

讨论了（Ｅ１,ｄ△ｐ）中的收敛序列的极限唯一性问题及λ截集的一致有界问题,证明了（Ｅ１,ｄ△ｐ ）中的单调有界序列的极限存在定理及夹逼定理。     

Bundles over Quantum Sphere and Noncommutative Index Theorem

The Noncommutative Index Theorem is used to prove that the Chern numbers of quantum Hopf line bundles over the standard Podle quantum sphere equal the winding numbers of the representations defining these bundles. This result gives an estimate of the positive cone of the algebraic K₀ of the standard quantum sphere.     

Kirszbraun's Theorem and Metric Spaces of Bounded Curvature

We generalize Kirszbraun's extension theorem for Lipschitz maps between (subsets of) euclidean spaces to metric spaces with upper or lower curvature bounds in the sense of A.D. Alexandrov. As a by-product we develop new tools in the theory of tangent cones of these spaces and obtain new characterization results which may be of independent interest. Submitted: June 1996, final version: November 1996     

The De Rham Decomposition Theorem For Metric Spaces

We generalize the classical de Rham decomposition theorem for Riemannian manifolds to the setting of geodesic metric spaces of finite dimension. Received: May 2006 Accepted: December 2006     

模糊度量空间上的不动模糊点定理

本文给出并证明了模糊度量空间的几个不动模糊点定理。     

一般赋范空间上连续函数的Korovkin型定理

本文引入一种连续模的新的控制泛函，利用直接方法（避免使用Ｋ－泛函）得到了一般赋范空间上连续函数的Ｋｏｒｏｖｋｉｎ型定理，得到的结果与Ｈ．Ｇｏｎｓｋａ用Ｋ－泛函得到的结果相比各有优点。     

凸度量空间非自混合映射的共同点定理

该文得到了凸度量空间上混合映射的共同点的一些结果.推广了Ciric在文献[3]中的结论.     

一个线性组合定理的证明

利用初等行变换与初等矩阵的关系,可证明线性组合定理：初等行变换不改变矩阵中列向量的线性关系.     

一个新的Ky Fan匹配定理及其在L-凸度量空间中的应用

建立了转移开覆盖的一个新的Ky Fan型匹配定理．作为应用，获得了Fan-Browder重合定理，不动点定理、极大元定理，相交定理和截口定理．     

Fuzzy度量空间中Fuzzy映象的重合定理与Ekeland‘s变分原理

本文给出了Ｆｕｚｚｙ度量空间中Ｆｕｚｚｙ映射的重合定理，推广了文（３）（５）中主要的结果。     

A Fixed Point Theorem in Intuitionistic Fuzzy Metric Spaces by Using New Commutativity Condition

We prove a common fixed point theorem for discontinuous,noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces by using a new commutativity condition.We validate our main result by an example.     

G-凸度量空间中的广义KKM定理及其应用

在一类新的G-凸度量空间中建立了一类新的KKM定理,统一、改进和发展了文献中的相应结果.作为应用,得到了几个新的匹配定理和不动点定理.     

非紧L-凸度量空间中的GLsKKM定理及其对不动点问题的应用

建立了非紧完备L-凸度量空间中的GLsKKM定理.作为应用,获得了Ky Fan 截口定理,极大元定理和Fan-Browder型不动点定理.