点集拓扑学

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。

The curriculum comprises the fundamental concepts of point set topology, differential manifold and differential dynamics, followed by the conceptions and theoretical methods of abrupt change, bifurcation, chaos and fractal. The analysis and compare combined with the practice in power system make it easy for readers to learn the basic methods of nonlinear dynamics and write high quality papers.

本课程主要内容包括点集拓扑学、微分流形和微分动力系统的基本概念，后面部分主要涉及到突变与分叉、混沌、分形和分维概念和理论方法，并结合电力系统实际例子加以分析与比较，使读者很快掌握非线性动力学的基本方法，能够写出高质量的文章和学术论文。

Subsequent chapters develop measure theory, point-set topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces

制定措施以后各章的理论，点集拓扑学，傅立叶的勒贝格积分系列，与Banach和Hilbert空间的基本知识

This course will focus on some fundamental knowledge and methods of general topology and algebraic topology, including the theory of topological spaces, continuous maps, fundamental group, the theory of covering spaces and simplicial homology and so on.

本课程将着重介绍点集拓扑学和代数拓扑学的一些基本知识和基本方法，包括拓扑空间理论、连续映射、基本群、覆盖空间理论和单纯同调群理论等。

In the past,description on topological spatial relationship of GIS was based on basic theory of point set topology.

过去对GIS拓扑空间关系的描述均是基于点集拓扑学的基本理论，描述点、线、面、体间的覆盖、相邻、相交和相离等关系。

The topological bodies were introduced to express the topological relationships between complicated objects based on the point set topology.

5基于点集拓扑学理论，引入了拓扑体来描述矿山复杂对象间的拓扑关系。

The dissertation gives a self-contained definition of Complex boundary and interior based on point set topology so that the Complex was consistent with the common description of spatial objects. It is in favor of a unifying between nature description and theory representation of spatial entities in 3DGIS.

本文基于点集拓扑学理论，对复形的边界和内部进行了完备性定义，使得空间实体的复形表达符合人类对空间对象的直观认识，有助于在3DGIS中实现空间实体的自然描述与理论表达的统一。

Based on the profound analysis for representation and reasoning of qualitative spatial relations, this paper proceeds with some originality innovation researches as follows:(1) Representation of spatial topological relations Based on the point-set topology and ontology, representation methods for spatial topological relations are researched.

在对定性空间关系表示与推理进行深入分析的基础上，本文进行了以下几方面的创新性研究：(1)空间拓扑关系表示以点集拓扑学和本体论为基础，研究了空间拓扑关系表示方法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。