8. Algebraic Topology
The sixth general mathematical framework is that of algebraic topology, which involves using the concepts and tools of abstract algebra to study topological spaces.
8.1 Betti numbers
Definition (Betti numbers). The k-th Betti number (k-dimensional Betti number) of a subset of A non-empty number is an integer denoted by β k (k = 0,.., n). In two dimensions: β 0 is the number of connected components and β 1 is the number of holes (i.e., cavities). In three dimensions: β...
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Algebraic Topology
Dimension Theory I: Vector Dimension and Topological Dimension
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