拓扑代数

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differ tial equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

Firstly, we establish a topological space associated to the derived category of a finite dimensional algebra with finite global dimension, which is a generalization of module variety and complex variety.

首先，我们在有限整体维数的代数的复形范畴上建立了复形拓扑空间。

Further more,we prove that the cohomotopy groups is isomorphic to K1 -group of the continuous algebra on topological boundary of bounded domains in C.

进一步证明了：在复平面C中，任意有界域的拓扑边界上连续函数代数的K_1-群与其边界上的上同伦群同构。

This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas.

这有提供非常直接的代数的入口方面的优势，和对组合的拓扑，以及物理想法。

This Handbook deals with the foundations of incidence geometry, in relationship with division rings, rings, algebras, lattices, groups, topology, graphs, logic and its autonomous development from various viewpoints.

这本手册涉及发生几何学的基础，在有划分戒指，戒指，代数，格子，组，拓扑，图，来自各种各样的观点的逻辑学和它的自治发展的关系里。

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

For detail,we studied the Incidence Algebra I defined by finite Partially Ordered Set X,and sheaf F based on the topology T_x defined by the partial order;By studying the relation between finite module category mod I and the sheaf category Sh_x A,we proved that they are equivalent.

特别的，对给定的有限偏序集X确定的Incidence代数Ⅰ，及由X的序关系定义的拓扑结构T_X上的层F，通过考查有限模范畴modⅠ与层范畴Sh_XA之间的关系，证明了Incidence代数上的模范畴与层范畴的等价性。

As a matter of fact we develop our study in the more general and more natural context of a theory ~ internally defined with respect to a topos of sheaves on a frame (i.e. a complete Heyting algebra; for example the algebra of open subsets of a topological space).

作为一个事实上我们在发展中的一个理论更普遍，更自然的环境研究国内关于对一帧的捆一topos中定义的（即完全Heyting代数，例如以开放的子集代数拓扑空间）。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷