The Fundamental Group
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 C2 and C3 are homotopic to each other and C1 is homotopic to a constant path. Path C1 is not homotopic to either C2 or C3 since neither C2 nor C3 can be pulled across the hole that they enclose.
KeywordsBase Point Fundamental Group Homotopy Class Terminal Point Covering Path
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