topology: Branches of Topology

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Encyclopedia—topology

Branches of Topology

Topology may be roughly divided into point-set topology, which considers figures as sets of points having such properties as being open or closed, compact, connected, and so forth; combinatorial topology, which, in contrast to point-set topology, considers figures as combinations (complexes) of simple figures (simplexes) joined together in a regular manner; and algebraic topology, which makes extensive use of algebraic methods, particularly those of group theory. There is considerable overlap among these branches.

Sections in this article:

Introduction
Branches of Topology
Continuous Transformations and Equivalent Figures
Topological Properties

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