Abstract
The main objective is to investigate the structure of a topological space through paths in space. More precisely, given a topological space $ X $ and $ x_0 $ a point of $ X $, associate through closed paths in $ X $ a group denoted by $ \ pi_1 (X, x_0) $ or $ \ pi_1 (X) $ (when space is pathwise connected) called the fundamental group of $ X $. Using such a group, some problems on topolog…