fundamental group

Definitions

1. 1

   For a specified topological space, the group whose elements are homotopy classes of loops…

   For a specified topological space, the group whose elements are homotopy classes of loops (images of some arbitrary closed interval whose endpoints are both mapped to a designated point) and whose group operation is concatenation.

   • From the definition it will be clear the group is a topological invariant of X; i.e., if two spaces are homeomorphic, their fundamental groups are isomorphic.
   • During the more than 100 years of its existence, the notion of the fundamental group has undergone a considerable evolution.

The neighborhood