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1·Algebraic topology is the study of the global properties of Spaces by means of algebra.

代数学的拓扑是透过代数空间的全球特性的研究。

2·Algebraic Topology; Symplectic Geometry and Topology; Ordinary and Partial Differential Equations.

代数拓扑；辛几何与拓扑；常微分和偏微分方程。

3·Some more advanced algebraic topology may also be useful as might some knowledge of category theory.

更深入的代数拓扑学以及范畴理论的知识将有更大的帮助。

4·Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology.

同胚映射和同伦等价是代数拓扑学中的两个重要概念。

5·Knowledge of elementary algebraic topology and elementary differential geometry is recommended, but not required.

建议事先知道一些关于代数拓扑和微分几何的基本知识，但不是必需的。

6·Topology is traditionally decomposed into three parts: General topology, Algebraic topology and Differential topology.

习惯上拓扑学被分成点集拓扑、代数拓扑和微分拓扑三部分。

7·An identification edge structure is put forward to represent non manifold modeling, which is built on the concepts and methods of the complex and CW complex in algebraic topology.

提出了一个非流形结构的表示方法——粘合边结构，其数学基础是代数拓扑中的复形理论。

8·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.

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。