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词汇 General topology
分类 英语词汇 英语翻译词典
释义

General topology

中文百科

点集拓扑学

点集拓扑学（Point Set Topology），有时也被称为一般拓扑学（General Topology），是数学的拓扑学的一个分支。它研究拓扑空间以及定义在其上的数学结构的基本性质。这一分支起源于以下几个领域：对实数轴上点集的细致研究，流形的概念，度量空间的概念，以及早期的泛函分析。它的表述形式大概在1940年左右就已经成文化了。通过这种可以为所有数学分支适用的表述形式，点集拓扑学基本上抓住了所有的对连续性的直观认识。

英语百科

General topology 点集拓扑学

The Topologist's sine curve, a useful example in point-set topology. It is connected but not path-connected.
This subspace of R² is path-connected, because a path can be drawn between any two points in the space.
Three iterations of a Peano curve construction, whose limit is a space-filling curve. The Peano curve is studied in continuum theory, a branch of general topology.

In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.
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