\(\def\Real{\mathbb{R}}\)

Homology.

Simplicial complexes; definition of simplicial homology. Basic properties. Functoriality.

Geometric realizations; simplicial approximations.

Homotopy invariance.

Euler calculus.

Additivity; Euler characteristic as measure. Integrals with respect to Euler characteristics.

Properties: linearity, Fubini theorem.

Classes of admissible sets.

Applications in …