Introduction to Topology

Introduction to Topology; By Colorado State University; Free Download: https://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf.

Topology is a branch of mathematics that focuses on the properties of space that are preserved under continuous deformations, but not necessarily under rigid transformations like stretching or bending. It’s concerned with the study of concepts like continuity, compactness, connectedness, and convergence, without relying on notions of distance or measurement. Topology classifies shapes and spaces by their essential geometric properties, leading to a deeper understanding of their fundamental structure. This field has applications in various areas, including physics, biology, and data analysis.

《拓扑简介》科罗拉多州立大学，免费下载： https://www.math.colostate.edu/~renzo/teaching/Topology10/Notes.pdf.

拓扑学是数学的一个分支，专注于在连续变形下保留的空间属性，但不一定在拉伸或弯曲等刚性变换下保留。它涉及连续性、紧凑性、连通性和收敛性等概念的研究，而不依赖于距离或测量的概念。拓扑学根据形状和空间的基本几何属性对形状和空间进行分类，从而更深入地了解其基本结构。该领域在各个领域都有应用，包括物理、生物学和数据分析。

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