In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when Topological invariant#T of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions such as simplicial complexes. After the proof of the simplicial approximation theorem this approach provided rigour.
The change of name, probably in the 1930s, reflected the move to organise topological classes such as cycles modulo boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence.