Basic Concepts of Algebraic Topology pp 60-82 | Cite as

# The Fundamental Group

Chapter

## Abstract

We turn now to the investigation of the structure of a topological space by means of paths or curves in the space. Recall that in Chapter 1 we decided that two closed paths in a space are homotopic provided that each of them can be “continuously deformed into the other.” In Figure 4.1, for example, paths *C*_{2} and *C*_{3} are homotopic to each other and *C*_{1} is homotopic to a constant path. Path *C*_{1} is not homotopic to either *C*_{2} or *C*_{3} since neither *C*_{2} nor *C*_{3} can be pulled across the hole that they enclose.

## Keywords

Base Point Fundamental Group Homotopy Class Terminal Point Covering Path
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag, New York Inc. 1978