代数拓扑学

流动性是国债二级市场的生命力。在代数拓扑学中J。

Mobility is the life of the second rank market . In algebraic topology , J.

本文首先利用代数拓扑学的思想，给出了拓扑结构聚类分析方法；

In this paper , first , We give a topologically structural cluster analysis method by using algebraic topology .

在代数拓扑学中J。

On Geographical Science In algebraic topology , J.

同胚映射和同伦等价是代数拓扑学中的两个重要概念。

To learn English Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology .

同伦是代数拓扑学中的概念，同伦算法已应用于一些工程实际问题的求解。

Homotopy is a concept of algebra topology , and homotopy algorithm has been applied to solving the practical problems .

在代数拓扑学中，人们不仅对重合点的存在感兴趣，也十分关注重合点的个数估计以及重合点的分类情况。

In algebraic topology , ones pay much attention to not only the existence of the coincidence points but also the estimation of their number and classification .

工业产品几何造型技术的发展要求，以及代数拓扑学复形等概念引入到几何造型中，因此产生了非流形几何造型理论。

With the request of geometry modeling system and application of the concept about complexes algebraictopology in the field of industrial production , the theory of non-manifold model come into being .

利用指数对应定理，将关于商映射的一个定理推广到上诱导拓扑的情形，并给出其在代数拓扑学中的若干应用。

Used the theorem of exponential correspondence , a theorem on quotient map was generalized to the cases of coinduced topology , and some applications of it in algebraic topology were also discussed .

应用代数拓扑学中周期变换的理论，将球面到欧氏空间的映射推广到从球面到光滑流形映射的情形，从而得到了Brosuk－Ulam型定理。

This paper makes an extension of the map from a sphere into an euclidean space to the mapof a sphere into a smooth manifold by means of the cyclic transformation theory of algebraic topology , gaining Borsuk-Ulam type of theorem .

自从1945年MacLane与Eilenberg提出范畴的概念和理论以来，它在数学的许多分支，例如代数几何学、拓扑学、微分几何学以及函数理论中均已有所应用。

In 1945 MacLane and Eilenberg introduced the concept and theories of categories , which have played a role in many branches of mathematics such as algebraic geometry , topology , differential geometry and functional theories .

学生需要对交换代数和基本拓扑学有一定的了解。

Students should have some familiarity with commutative algebra and basic topology .

本文给出了联系拓扑分子格理论的两类特殊的Boole代数，进而从拓扑学的角度，对A。

This paper enumerates two special classes of Boole algebras related to the theory of topological molecular Lattices , and then , from the viewpoint of topology , expands slightly the representation theorem on atomic Boole algebra which was first proved by A.