Date: 2024-02-25 | Article ID: 28539 |

Homology groups are examples of topological invariants: topologically equivalent spaces have the same homology groups. The idea behind homology groups is to consider a special family of topological spaces C for which the concept of a *boundary* makes sense, namely spaces made of simple polyhedra, and to use maps from those spaces into another topological space X as a way of exploring the topology of X. Roughly, the nth **homology group** of X describes continuous maps into X from those special n-dimensional spaces C that cannot be extended to a continuous map into X from any of the special (n+1)-dimensional spaces whose boundary is C.

**2024-02-25**(first version)

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