Topología y álgebra: hasta que la muerte las separe

A fundamental topological problem entails deciding when two topological spaces are homeomorphic. In general, an algorithmic method does not exist that can resolve this problem. Attempting to prove that two spaces are homeomorphic may result in a task that is essentially mechanical. The precise object of this work is to construct a manageable algebraic model (the fundamental group) that detects the presence or absence of topological properties in spaces.