- A definition for General Topology is Geometry of Sets, and the 1 to 1 and onto. A detail properties must be continuous (one to one correspondence), Compact, connected (onto)
- Algebraic Topology considers homology (one to one correspondence) a manifold is not a Circle. Homotopy record their properties can be consider onto.
- Differential Topology considers the Geometry of the Manifolds
- Geometric Topology considers manifolds and maps (one to one correspondence) between them, particularly embeddings of one manifold into another.
